Nichomauss' Theorem states that can be written as the sum of consecutive integers, thus giving us .
A Visual Proof
Imagine a cuboid with a height of , and length and width of . Divide it into unit cubes. Now, starting from the bottom right of the cuboid (when it's flat on the ground), imagine the first cube to have (call this ). Now, extend its length and width by to get another cuboid with and (call this ). Color yellow and blue. Now, it's easy to see that has unit cubes and has unit cube. We can then rearrange the unit cubes into a cube. Thus, we clearly have . And we can continue this process to unit cubes and cuboids with , , which gets us to .