Hilbert-Waring Theorem/Variant Form/Particular Cases/7

Particular Case of the Hilbert-Waring Theorem -- Variant Form: $k = 7$
The Hilbert-Waring Theorem -- Variant Form states that:

The case where $k = 7$ is:

Every sufficiently large positive integer can be expressed as the sum of a number of positive $7$th powers.

The exact number is the subject of ongoing research, but at the time of writing ($20$th December $2018$) it is known that it is between $8$ and $33$.

That is:
 * $8 \le \map G 3 \le 33$