$a^2+b^2=c^2$ is related to right triangles - how the sums of the squares of the legs equals the square of the hypotenuse.
What about the following sum of cubes?
Is there a geometric interpretation for this, like there is with the Pythagorean theorem? Is there some shape that embodies this equation, like a right triangle does for $a^2+b^2=c^2$? Would it involve sums of volumes of certain cubes?