Let me assume that the whole construction is like a plus sign, with all spheres identical and at the same distance d to the centre.

Let I be the moment of inertia of such a sphere around the centre (I suppose you need the parallel axis theorem and it will be something like I = I_{sphere} + m d^{2}, but that's irrelevant). Then when you rotate around the y-axis, only two of the spheres are moving, so you will get something like
I_{tot} = 2I.
When you rotate around the z-axis, all four are moving and you have
I_{tot} = 4I.

Since the work-energy theorem states that the work W is proportional to I_{tot}, the conclusion would follow.