# Integer as Sum of 4 Cubes

## Theorem

Let $n \in \Z$ be an integer.

Let $n \not \equiv 4 \pmod 9$ and $n \not \equiv 5 \pmod 9$.

Then it is possible to express $n$ as the sum of no more than $4$ cubes which may be either positive or negative.

## Examples

### $23$ as Sum of $4$ Cubes

$23 = 8 + 8 + 8 - 1 = 2^3 + 2^3 + 2^3 + \left({-1}\right)^3$