Perfect Cube Number Calculator

Input a number to check if it's a perfect cube, or specify a range to generate all perfect cubes within it.

Perfect Cube Check or Generate

What Is a Perfect Cube?

A perfect cube is a non-negative integer that can be expressed as the cube of an integer. In other words, if there exists an integer \(n\) such that \(n^3 = x\), then \(x\) is a perfect cube.

How to Determine if a Number Is a Perfect Cube

  1. Ensure the number \(x\) is a positive integer.
  2. Calculate the cube root of \(x\), \(n = \sqrt[3]{x}\).
  3. Verify whether \(n\) is an integer. If \(n^3 = x\), the number is a perfect cube; otherwise, it is not.

Examples

Example 1: Is 20 a Perfect Cube?

Solution:

Compute \(n = \sqrt[3]{20} \approx 2.71\).

\(2.71\) is not an integer.

Result: 20 is not a perfect cube.

Example 2: Is 125 a Perfect Cube?

Solution:

Compute \(n = \sqrt[3]{125} = 5\).

\(5^3 = 125\).

Result: 125 is a perfect cube.

Example 3: Is 1000 a Perfect Cube?

Solution:

Compute \(n = \sqrt[3]{1000} = 10\).

\(10^3 = 1000\).

Result: 1000 is a perfect cube.

First 100 Perfect Cubes

  • 1
  • 8
  • 27
  • 64
  • 125
  • 216
  • 343
  • 512
  • 729
  • 1000
  • 1331
  • 1728
  • 2197
  • 2744
  • 3375
  • 4096
  • 4913
  • 5832
  • 6859
  • 8000
  • 9261
  • 10648
  • 12167
  • 13824
  • 15625
  • 17576
  • 19683
  • 21952
  • 24389
  • 27000
  • 29791
  • 32768
  • 35937
  • 39304
  • 42875
  • 46656
  • 50653
  • 54872
  • 59319
  • 64000
  • 68921
  • 74088
  • 79507
  • 85184
  • 91125
  • 97336
  • 103823
  • 110592
  • 117649
  • 125000
  • 132651
  • 140608
  • 148877
  • 157464
  • 166375
  • 175616
  • 185193
  • 195112
  • 205379
  • 216000
  • 226981
  • 238328
  • 250047
  • 262144
  • 274625
  • 287496
  • 300763
  • 314432
  • 328509
  • 343000
  • 357911
  • 373248
  • 389017
  • 405224
  • 421875
  • 438976
  • 456533
  • 474552
  • 493039
  • 512000
  • 531441
  • 551368
  • 571787
  • 592704
  • 614125
  • 636056
  • 658503
  • 681472
  • 704969
  • 729000
  • 753571
  • 778688
  • 804357
  • 830584
  • 857375
  • 884736
  • 912673
  • 941192
  • 970299
  • 1000000