Is N a Perfect Cube? Calculator
Perfect Cube Checker
Use the checker above to determine whether any integer is a perfect cube. A perfect cube is an integer of the form k³ for some integer k. Unlike perfect squares, perfect cubes can be negative: since (-k)³ = -k³, every negative integer whose absolute value is a perfect cube is itself a perfect cube. The first non-negative perfect cubes are 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, ...
What Is a Perfect Cube?
A perfect cube is an integer that is the cube of an integer:
n is a perfect cube ⇔ n = k3, k ∈ ℤ
Equivalently, n is a perfect cube if and only if ∛n is an integer. Geometrically, you can arrange n identical unit cubes into a cubic grid only if n is a non-negative perfect cube.
Signs: Unlike perfect squares (which are always non-negative), perfect cubes can be negative. Examples of negative perfect cubes: -1 = (-1)³, -8 = (-2)³, -27 = (-3)³, -64 = (-4)³, -125 = (-5)³.
Prime-factorization rule: |n| is a perfect cube iff every prime in its prime factorization appears with an exponent divisible by 3. For example, 216 = 23 × 33 (both divisible by 3) is a perfect cube; 72 = 23 × 32 has exponent 2 on 3, so it is not.
Common Examples
Perfect Cubes from 0³ to 20³
The numbers 0, 1, 8, 27, 64, ..., 8000 are the perfect cubes from 0³ to 20³. Click any number below to see its check page.
Popular Perfect-Cube Checks
Common ‘Is N a perfect cube?’ queries — click any to see the step-by-step verdict (includes negative cubes):
Related Calculators
- Cube Root Calculator (∛n) — decimal value with step-by-step
- Simplify Cube Root — radical form
- Cubed Calculator (n³) — the inverse direction
- Is N a Perfect Square? — the square analog
- All Math Calculators