Perfect Cube Definition
A perfect cube is a number that results from multiplying an integer by itself three times. In other words, if we can write a number N as:
N = a × a × a = a³
where a is an integer (whole number), then N is a perfect cube.
Unlike square roots, cube roots can be found for negative numbers too! For example, (−2)³ = −8, so −8 is a perfect cube.
How Do We Use the Perfect Cube Calculator?
Simply enter any integer into the Number field and press Check. The calculator will instantly tell you:
- Whether the number is or is not a perfect cube
- The cube root if it is a perfect cube (e.g., ∛125 = 5)
- The verification formula (e.g., 5 × 5 × 5 = 5³ = 125)
- The cube of the entered number (N³)
- A table of nearby perfect cubes for context
Measurement System Options
The calculator supports three unit contexts in addition to plain numbers:
- Metric Volume — mm³, cm³, dm³, m³, km³. Useful for checking whether a volume is a perfect cube (e.g., 27 m³ → cube side = 3 m).
- US Imperial Volume — in³, ft³, yd³. Perfect for construction, packaging, or engineering tasks.
- Currency — USD ($), RUB (₽), EUR (€), GBP (£), JPY (¥), CAD, AUD, CHF, CNY, BRL, MXN, INR, KRW, TRY, SAR. Check whether a price or financial amount is a perfect cube number.
Which Numbers Are Perfect Cubes?
Here are some examples of perfect cubes and non-perfect cubes:
- 2³ = 2 × 2 × 2 = 8 → 8 is a perfect cube
- (−2)³ = (−2) × (−2) × (−2) = −8 → −8 is also a perfect cube
- 6³ = 6 × 6 × 6 = 216 → 216 is a perfect cube
- ∛100 ≈ 4.64 (not an integer) → 100 is NOT a perfect cube
- (−10)³ = −1000 → −1000 is a perfect cube
- ∛125,000 = 50 → 125,000 is a perfect cube
List of Perfect Cubes (1 to 10)
| Number (n) | Perfect Cube (n³) |
|---|---|
| 1 | 1 |
| 2 | 8 |
| 3 | 27 |
| 4 | 64 |
| 5 | 125 |
| 6 | 216 |
| 7 | 343 |
| 8 | 512 |
| 9 | 729 |
| 10 | 1,000 |
FAQs
Is 0 a perfect cube?
Yes! 0 = 0³, so 0 is a perfect cube with a cube root of 0.
Can negative numbers be perfect cubes?
Yes! Negative integers can be perfect cubes because multiplying a negative number by itself three times gives a negative result. For example, (−3)³ = −27, so −27 is a perfect cube.
Are perfect cubes related to perfect squares?
Both are special sets of integers. A number can be both a perfect square and a perfect cube — such numbers are called perfect sixth powers (e.g., 1, 64, 729...) because n⁶ = (n²)³ = (n³)².
How do I check if a large number is a perfect cube?
Use this calculator! For manual checking: find the approximate cube root using a calculator, round to the nearest integer, then cube it and verify. For example, ∛1,331 ≈ 11, and 11³ = 1,331 ✓
What is the cube root of a perfect cube used for?
The cube root of a perfect cube has many applications:
- Geometry — finding the side length of a cube given its volume
- Engineering — scale calculations in 3D design
- Number theory — studying properties of integers
- Finance — some financial formulas involve cube roots (e.g., geometric mean over 3 periods)