Question 385852
I'll assume that the spheres must take their own shape, without being altered.

I would imagine the answer being (4+3+2+1) + (3+2+1) + (2+1) + 1 = 20, obtained by starting with a triangle of spheres with 4 spheres to a side, and letting the side length go to 3, 2, 1. I'm not quite sure how to prove this...it'll definitely require much higher level mathematics.