Cubes of 1 to 30 range from 1³ = 1 to 30³ = 27,000. A cube of a number is the result of multiplying it by itself three times: n³ = n × n × n. Memorising cubes from 1 to 30 is essential for students preparing for competitive exams, board exams, and aptitude tests — it speeds up calculations in algebra, volume problems, and number theory. Among numbers 1 to 30, the perfect cubes are 1, 8, and 27 (since 1³ = 1, 2³ = 8, 3³ = 27). This guide provides the complete cubes of 1 to 30 table, shortcut tricks, interesting patterns, and solved examples.
Cubes of 1 to 30 range from 1³ = 1 to 30³ = 27,000.
A cube of a number n is n × n × n, written as n³.
The last digit of n³ depends only on the last digit of n (e.g., ends in 2 → cube ends in 8).
Sum of cubes formula: 1³ + 2³ + ... + n³ = [n(n+1)/2]².
Each cube n³ equals the sum of n consecutive odd numbers.
Cubes grow faster than squares: 30² = 900 but 30³ = 27,000.
Key cubes: 5³ = 125, 10³ = 1000, 15³ = 3375, 20³ = 8000, 25³ = 15625, 30³ = 27000.
To check if a number is a perfect cube, prime factorise it — all prime factors must appear in groups of 3.
Here is the complete table of cubes from 1 to 30:
1³ = 1 2³ = 8 3³ = 27 4³ = 64 5³ = 125 6³ = 216 7³ = 343 8³ = 512 9³ = 729 10³ = 1,000 11³ = 1,331 12³ = 1,728 13³ = 2,197 14³ = 2,744 15³ = 3,375 16³ = 4,096 17³ = 4,913 18³ = 5,832 19³ = 6,859 20³ = 8,000 21³ = 9,261 22³ = 10,648 23³ = 12,167 24³ = 13,824 25³ = 15,625 26³ = 17,576 27³ = 19,683 28³ = 21,952 29³ = 24,389 30³ = 27,000
For easier memorisation, here are the cubes grouped by tens:
1 to 10: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
11 to 20: 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000
21 to 30: 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000
Key cubes to remember: • 1³ = 1 • 5³ = 125 • 10³ = 1,000 • 15³ = 3,375 • 20³ = 8,000 • 25³ = 15,625 • 30³ = 27,000
Notice how quickly cubes grow: • 1³ = 1 (single digit) • 5³ = 125 (three digits) • 10³ = 1,000 (four digits) • 20³ = 8,000 (four digits) • 30³ = 27,000 (five digits)
Cubes grow much faster than squares: 30² = 900 but 30³ = 27,000 — that is 30 times larger.
Trick 1: Using (a + b)³ = a³ + 3a²b + 3ab² + b³ • 12³ = (10 + 2)³ = 1000 + 3(100)(2) + 3(10)(4) + 8 = 1000 + 600 + 120 + 8 = 1728 • 21³ = (20 + 1)³ = 8000 + 3(400)(1) + 3(20)(1) + 1 = 8000 + 1200 + 60 + 1 = 9261
Trick 2: Using (a − b)³ = a³ − 3a²b + 3ab² − b³ • 19³ = (20 − 1)³ = 8000 − 3(400)(1) + 3(20)(1) − 1 = 8000 − 1200 + 60 − 1 = 6859 • 28³ = (30 − 2)³ = 27000 − 3(900)(2) + 3(30)(4) − 8 = 27000 − 5400 + 360 − 8 = 21952
Trick 3: Using the previous cube n³ = (n−1)³ + 3(n−1)² + 3(n−1) + 1 • 11³ = 10³ + 3(100) + 3(10) + 1 = 1000 + 300 + 30 + 1 = 1331 • 26³ = 25³ + 3(625) + 3(25) + 1 = 15625 + 1875 + 75 + 1 = 17576
Trick 4: Cubes ending in 5 n³ always ends in 5 if n ends in 5. • 5³ = 125, 15³ = 3375, 25³ = 15625
Trick 5: Last digit pattern The last digit of n³ is always the same as the last digit of n. • 2³ = 8 → but 12³ = 1728 (ends in 8, same as 2³) • 7³ = 343 (ends in 3) → 17³ = 4913 (ends in 3) • Actually: the unit digit of n³ depends only on the unit digit of n.
Pattern 1: Last digit cycle The last digit of cubes follows the pattern based on the last digit of the number: • n ends in 0 → n³ ends in 0 (10³ = 1000, 20³ = 8000) • n ends in 1 → n³ ends in 1 (1³ = 1, 11³ = 1331, 21³ = 9261) • n ends in 2 → n³ ends in 8 (2³ = 8, 12³ = 1728, 22³ = 10648) • n ends in 3 → n³ ends in 7 (3³ = 27, 13³ = 2197, 23³ = 12167) • n ends in 4 → n³ ends in 4 (4³ = 64, 14³ = 2744, 24³ = 13824) • n ends in 5 → n³ ends in 5 (5³ = 125, 15³ = 3375, 25³ = 15625) • n ends in 6 → n³ ends in 6 (6³ = 216, 16³ = 4096, 26³ = 17576) • n ends in 7 → n³ ends in 3 (7³ = 343, 17³ = 4913, 27³ = 19683) • n ends in 8 → n³ ends in 2 (8³ = 512, 18³ = 5832, 28³ = 21952) • n ends in 9 → n³ ends in 9 (9³ = 729, 19³ = 6859, 29³ = 24389)
Pattern 2: Sum of consecutive odd numbers 1³ = 1 2³ = 3 + 5 = 8 3³ = 7 + 9 + 11 = 27 4³ = 13 + 15 + 17 + 19 = 64 n³ = sum of n consecutive odd numbers
Pattern 3: Sum of cubes formula 1³ + 2³ + 3³ + ... + n³ = [n(n+1)/2]² = (sum of first n natural numbers)² Example: 1³ + 2³ + 3³ = 1 + 8 + 27 = 36 = (3×4/2)² = 6² = 36 ✓
A perfect cube is a number that is the cube of a whole number.
Perfect cubes from 1 to 27000 (cubes of 1 to 30): 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000
Total: 30 perfect cubes
Cube roots of perfect cubes: ∛1 = 1, ∛8 = 2, ∛27 = 3, ∛64 = 4, ∛125 = 5 ∛216 = 6, ∛343 = 7, ∛512 = 8, ∛729 = 9, ∛1000 = 10 ∛1331 = 11, ∛1728 = 12, ∛2197 = 13, ∛2744 = 14, ∛3375 = 15 ∛4096 = 16, ∛4913 = 17, ∛5832 = 18, ∛6859 = 19, ∛8000 = 20 ∛9261 = 21, ∛10648 = 22, ∛12167 = 23, ∛13824 = 24, ∛15625 = 25 ∛17576 = 26, ∛19683 = 27, ∛21952 = 28, ∛24389 = 29, ∛27000 = 30
How to check if a number is a perfect cube:
Here is a comparison of squares and cubes for numbers 1 to 30:
n | n² (Square) | n³ (Cube) 1 | 1 | 1 2 | 4 | 8 3 | 9 | 27 4 | 16 | 64 5 | 25 | 125 6 | 36 | 216 7 | 49 | 343 8 | 64 | 512 9 | 81 | 729 10 | 100 | 1,000 12 | 144 | 1,728 15 | 225 | 3,375 20 | 400 | 8,000 25 | 625 | 15,625 30 | 900 | 27,000
Key observations: • Cubes grow much faster than squares • 30² = 900 but 30³ = 27,000 (30 times larger) • n³ = n × n² (cube = number × its square) • 4² = 16 and 4³ = 64 → only at n = 4 does n² start with the same digit as n³ (both start with digits leading to 64) • Both 2³ = 8 and 8³ = 512 → and 2² = 4 and 4³ = 64 — interesting connections
Example 1: Find 14³ without a calculator. Solution: 14³ = (15 − 1)³ = 3375 − 3(225)(1) + 3(15)(1) − 1 = 3375 − 675 + 45 − 1 = 2744
Example 2: Find 11³ + 19³. Solution: 11³ = 1331, 19³ = 6859. Sum = 1331 + 6859 = 8190
Example 3: Is 9261 a perfect cube? Solution: 9261 = 3 × 3087 = 3 × 3 × 1029 = 3 × 3 × 3 × 343 = 3³ × 7³ = (3 × 7)³ = 21³. Yes, 9261 is a perfect cube. ∛9261 = 21 ✓
Example 4: Find the volume of a cube with side 13 cm. Solution: Volume = side³ = 13³ = 2197 cm³
Example 5: Find 30³ − 29³. Solution: Using a³ − b³ = (a−b)(a² + ab + b²) 30³ − 29³ = (1)(900 + 870 + 841) = 2611 Verification: 27000 − 24389 = 2611 ✓
Example 6: Find 1³ + 2³ + 3³ + ... + 10³. Solution: Using formula: [n(n+1)/2]² = [10 × 11/2]² = 55² = 3025
Example 7: Simplify ∛(8000 ÷ 125). Solution: ∛(8000/125) = ∛64 = 4. Or: ∛8000 / ∛125 = 20/5 = 4
Example 8: Find the cube of 22 using (20+2)³. Solution: 22³ = 8000 + 3(400)(2) + 3(20)(4) + 8 = 8000 + 2400 + 240 + 8 = 10648
The cubes of 1 to 30 are: 1³=1, 2³=8, 3³=27, 4³=64, 5³=125, 6³=216, 7³=343, 8³=512, 9³=729, 10³=1000, 11³=1331, 12³=1728, 13³=2197, 14³=2744, 15³=3375, 16³=4096, 17³=4913, 18³=5832, 19³=6859, 20³=8000, 21³=9261, 22³=10648, 23³=12167, 24³=13824, 25³=15625, 26³=17576, 27³=19683, 28³=21952, 29³=24389, 30³=27000.
The cube of 25 is 15,625. Calculation: 25 × 25 × 25 = 15,625. Quick method: 25³ = (25)² × 25 = 625 × 25 = 15,625. Or: 25³ = (20+5)³ = 8000 + 3(400)(5) + 3(20)(25) + 125 = 8000 + 6000 + 1500 + 125 = 15,625.
The cube of 30 is 27,000. Calculation: 30 × 30 × 30 = 27,000. Quick method: 30³ = 3³ × 10³ = 27 × 1000 = 27,000. This is the largest cube in the 1 to 30 table.
Shortcut tricks: (1) Use (a+b)³ formula: 12³ = (10+2)³ = 1000+600+120+8 = 1728. (2) Use (a−b)³: 19³ = (20−1)³ = 8000−1200+60−1 = 6859. (3) From previous cube: n³ = (n−1)³ + 3(n−1)² + 3(n−1) + 1. (4) For multiples of 10: 20³ = 2³ × 10³ = 8 × 1000 = 8000.
The last digit of n³ depends on the last digit of n: 0→0, 1→1, 2→8, 3→7, 4→4, 5→5, 6→6, 7→3, 8→2, 9→9. Notice: 0,1,4,5,6,9 keep their last digit; 2↔8 and 3↔7 swap. This pattern repeats for all numbers — e.g., 22³ = 10648 (ends in 8 because 2→8).
The sum of cubes of first n natural numbers is: 1³ + 2³ + 3³ + ... + n³ = [n(n+1)/2]². This equals the square of the sum of first n numbers. Example: 1³+2³+3³+4³+5³ = 1+8+27+64+125 = 225 = [5×6/2]² = 15² = 225. Beautifully, the sum of cubes = (sum of numbers)².
Each cube n³ equals the sum of n consecutive odd numbers: 1³ = 1, 2³ = 3+5 = 8, 3³ = 7+9+11 = 27, 4³ = 13+15+17+19 = 64. The starting odd number for n³ is n²−n+1. For 5³: starts at 25−5+1 = 21, so 5³ = 21+23+25+27+29 = 125.
Method 1: Prime factorisation — if every prime factor appears in groups of 3, it is a perfect cube. Example: 1728 = 2⁶ × 3³ = (2²×3)³ = 12³ ✓. Method 2: Estimate using the table — 9261 is between 8000 (20³) and 10648 (22³), try 21³ = 9261 ✓. Method 3: Use a calculator to find the cube root.
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