Why Do Cubes Add Up To Squares?

A geometric demonstration of:

 

1^3 + 2^3 +...+ n^3 = [1+2+...+n]^2

 

You simply restack the 1 deep slabs in the top left of the square going from n=4 to n=5 to create the 5x5x5 cube, shown in the bottom right.

 

The next image shows how all 5 cubes are stacked from slices of a (1+2+3+4+5) square.

Done