Integer as Sum of Seven Positive Cubes/Historical Note

Historical Note on Integer as Sum of Seven Positive Cubes
knew that some integers required at least $9$ positive cubes to represent them as a sum:

In fact these are the only two integers that need as many as $9$ positive cubes to express them.

All other integers need no more than $8$.

It was shown in $1943$ by that only finitely many numbers do require $8$ positive cubes.

That is, from some point on, $7$ cubes are enough.

It is not known what that point is.