Charts & references · 3 min read
Cube Numbers and Cube Roots Chart (1 to 20)
The chart
| n | n³ | n | n³ |
|---|---|---|---|
| 1 | 1 | 11 | 1,331 |
| 2 | 8 | 12 | 1,728 |
| 3 | 27 | 13 | 2,197 |
| 4 | 64 | 14 | 2,744 |
| 5 | 125 | 15 | 3,375 |
| 6 | 216 | 16 | 4,096 |
| 7 | 343 | 17 | 4,913 |
| 8 | 512 | 18 | 5,832 |
| 9 | 729 | 19 | 6,859 |
| 10 | 1,000 | 20 | 8,000 |
Cube roots
The cube root undoes the cube: ∛729 = 9. Unlike square roots, cube roots exist for negative numbers: ∛(−27) = −3.
27^(1/3), the cube root of 27
Step-by-step working 3 steps
- 1Write it as a power
27^(1/3)
- 2Fractional exponent = root and power
27^(1/3) = (3th root of 27)^1
The denominator is the root, the numerator is the power.
- 3Result
27^0.333333 = 3
Cubes and volume
A cube with side 4 has volume 4³ = 64 and surface area 6 × 4² = 96. Try other sizes in the volume calculator.
Patterns
- Cubes of even numbers are even; cubes of odd numbers are odd.
- The last digit of n³ repeats in a cycle with n (1→1, 2→8, 3→7, 4→4, 5→5, 6→6, 7→3, 8→2, 9→9, 0→0).
- Sum of the first n cubes = (n(n+1)/2)²: for n = 5 that is 225, and 1 + 8 + 27 + 64 + 125 = 225.
Frequently asked questions
What is the cube root of 1000?
10, because 10 × 10 × 10 = 1000.
Can you cube a negative number?
Yes, and the result stays negative: (−2)³ = −8.
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