Perfect cube

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In mathematics, a perfect cube or cube number, is an integer that can be written as the cube (arithmetic) of some other integer. So for example, 8 is a cube number since it can be written as 2 × 2 × 2. Different from a square number, there is no smallest cube number, since negative integers are included. For example, (−4) × (−4) × (−4) = −64. A cube number, unlike square numbers, can end with any digit. If the last digit is 2 or 6 the digit before must be odd, and if the last digit before is 4 or 8 the preceding digit must be even. For 3,1,7,and 9, the digit before can be even or odd. For 5, the digit before is 2 or 7.

Some cube numbers are also square numbers, for example 64 is a square number (8 × 8) and a cube number (4 × 4 × 4); this happens if and only if it is a perfect sixth power.

A 3x3x3 Rubik's Cube composed of 27 smaller cubes

The number m is a perfect cube if and only if one can arrange m points in a cube, for example 3 × 3 × 3 = 27.

The sum of the first n perfect cubes is the nth triangle number squared. For example, the sum of the first five perfect cubes, 1^3 + 2^3 + 3^3 + 4^3 + 5^3, is equal to sum of the 5th triangular number squared, namely 15^2 which is 225.

Perfect cube

See also