combinatorics - Combinatorial reasoning for the identity $left ( sum_{i=1}^n i right )^2 = left ( sum_{i=1}^n i^3 right ) $

There is the interesting identity:

$$\left ( \sum_{i=1}^n i \right )^2 = \left ( \sum_{i=1}^n i^3 \right ) $$
which holds for any positive integer $n$.

I know several was of proving this (finite differences, induction, algebraic tricks etc..), but even so I still find it "weird" that it is even true.

Is there a very nice intuitive way to prove this using some kind of combinatorial argument? (Like the why the sum of the volume of the first $n$ cubes should be the area of ... not sure here?)

If you have any pretty different proof that could be enlightening I would love to see it.

Thanks a lot!