Cubes which are Sum of Three Cubes

Theorem
The following cube numbers can be expressed as the sum of $3$ positive cube numbers:
 * $6^3, 9^3, 12^3, 18^3, 19^3, 20^3, 24^3, 25^3, \ldots$

The associated cube roots:
 * $6, 9, 12, 18, 19, 20, 24, 25, \ldots$