So in general, suppose your square is x squares across and your cube is y cubes across. The square has 4(x-1) small squares on the outside, and (x-2)^2 on the inside right? If you find a similar formula for the cube, you can compare the two and see exactly when one ratio is bigger than the other.
What exactly do you mean by this question?
Well the diameter of a unit square is √2, and the diameter of a unit cube is √3. You probably meant the side length when you say "diameter".