cannonball stacking | cannonball stacking problem

Find a way to stack a square of cannonballs laid out on the ground into a square pyramid (i.e., find a square number which is also square pyramidal). This corresponds to solving the Diophantine equation sum_(i = 1)^k i^2 = 1/6 k(1 + k)(1 + 2k) = N^2 for some pyramid height k.

sphere packing | square number | square pyramid | square pyramidal number