Perfect cubes – 1, 8, 27, 64, 125 … – are the volumes of cubes with whole-number sides. Recognising them helps with simplifying cube roots and factoring sums and differences of cubes.
How to use the Perfect Cube Calculator
- Number
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The integer cube root is computed exactly and cubed again to test. The prime factorisation is shown too: in a perfect cube every exponent is divisible by 3.
Formula
N is a perfect cube ⇔ N = a³ for some integer a ⇔ every prime exponent is a multiple of 3
Worked example
Inputs — Number: 125.
Results — Result = 125 is a perfect cube: 5³ = 125; Cube root = 5; Prime factorisation = 5³.
Key terms
- Perfect cube
- The cube of an integer.
Frequently asked questions
Is 1,000 a perfect cube?
Yes: 10³.
Can a negative number be a perfect cube?
Yes: −27 = (−3)³.
How do I recognise a perfect cube from its prime factors?
Every exponent is a multiple of 3, e.g. 216 = 2³ × 3³.
What are the first ten cubes?
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.