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Perfect Cube Checker

Instantly test if a number is a perfect cube.

How it is calculated

A perfect cube is a whole number equal to k³ for some whole number k. The tool takes the cube root of the number, rounds it to the nearest whole number k, cubes that back and compares: is cube ⇔ k³ = n. It shows Yes or No, the rounded root k and its cube k³, so for a non-cube you see the closest cube for reference. Negative numbers work, because an odd power keeps the sign: −64 = (−4)³ counts as a cube. Zero and one are cubes too. Only whole numbers are accepted: a decimal such as 27.5 shows no result instead of being cut down, and so does anything with an absolute value above 9,007,199,254,740,992 (253) or text that is not a number.

Worked example

Test n = 216. The cube root of 216 is 6.000, which rounds to 6. Cube it back: 6 × 6 × 6 = 216. That equals the input, so the answer is Yes: nearest cube root 6, nearest cube 216. Now test 200. Its cube root is about 5.85, which rounds to 6, and 6³ = 216 is not 200, so the tool says No and still shows 6 and 216 as the nearest root and cube.

Try this example →

Common mistakes

  • Typing a decimal such as 27.5 and expecting a Yes or No. The checker only works on whole numbers, so a fractional value gives no result.
  • Thinking negatives are never cubes. Unlike squares, cubes can be negative, so −8 is a perfect cube (−2)³ and the tool says Yes.
  • Confusing a perfect cube with a perfect square. 16 is a square but not a cube, while 8 is a cube but not a square. Only 0, 1, 64, 729 and similar sixth powers are both.
  • Reading the nearest cube as a factor or answer when the result is No. For a non-cube, the nearest root and cube are simply the closest ones.
  • Entering numbers beyond about 9 quadrillion, such as 1e30. These are rejected, so such a value cannot be checked here.

About this calculator

A perfect cube is an integer that results from cubing another integer — 27 is a perfect cube because 3³ = 27, but 28 is not, since no whole number cubed produces it. The check works by taking the cube root of the input, rounding it to the nearest integer, cubing that rounded value back, and comparing it against the original number; if they match, the number is a perfect cube.

This kind of integer property test appears throughout number theory education as a building block for understanding factorization and exponents, in programming interview questions that ask candidates to detect perfect powers efficiently, and in recreational and competitive mathematics puzzles that rely on properties of cubes, such as sum-of-cubes and cube-difference problems. Cube roots and perfect cubes also come up in geometry when reasoning about the side length of a cube given its volume.

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