In fact it seems that the diameter 3 balls are most efficient only for cubes of edge-length between 3 and 2+sqrt(2) = 3.414.... These are the sizes for which you can fit in 1 diameter 3 ball, but can't fit in 4 diameter 2 balls. Above that, diameter 2 balls are more efficient (except that a cube of edge-length 6 can fit in the same volume either way; 27 diameter 2 balls or 8 diameter 3 balls).

> Since 27×3^3 = 729 and 8×2^3 = 800

I think you mean 100 x 2^3 = 800. But, yer correct that’s what I get from using a half remembered example without checking.