Hilbert-Waring Theorem/Particular Cases/3

Particular Case of the Hilbert-Waring Theorem: $k = 3$
The Hilbert-Waring Theorem states that:

The case where $k = 3$ is:

Every positive integer can be expressed as the sum of at most $9$ positive cubes.

That is:
 * $\map g 3 = 9$