Cube (algebra)

The difference between the cubes of consecutive integers can be expressed as follows:

There is no minimum perfect cube, since the cube of a negative integer is negative. For example, (−4) × (−4) × (−4) = −64.

Every positive integer can be written as the sum of nine (or fewer) positive cubes. This upper limit of nine cubes cannot be reduced because, for example, 23 cannot be written as the sum of fewer than nine positive cubes:

Visual demonstration that the square of a triangular number equals a sum of cubes.

For example, the sum of the first 5 cubes is the square of the 5th triangular number,

There are examples of cubes of numbers in arithmetic progression whose sum is a cube: