Hilbert-Waring Theorem/Variant Form/Particular Cases/3

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

The case where $k = 3$ is:

Every sufficiently large positive integer can be expressed as the sum of a number of positive cubes.

The exact number is still subject to research, but at the time of writing ($11$th February $2017$) it is known that it is between $4$ and $7$.

That is:
 * $4 \le G \left({3}\right) \le 7$