I did see a third setup where you take Σ (i = 1 to n) (Σ (k = 1 to i) 2k-1), which is a valid setup where you count all the blocks on the top of their column, then remove those and count the new top blocks, etc - but it ended up not leading to a proof of the formula because as it turns out, there are always i^2 (from i = n to 1) blocks on the top layer. So it's just a worse way of doing Σi^2 and we get a 0 = 0 situation.