elementary number theory - Geometrical intuition for sum of first n cubes

The relation

$$\sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k\right)^2$$

baffled me when I first found out (i.e. yesterday on a train trip). Writing an inductive proof is easy and I know that there is a recursive way to obtain a general formula for

$$\sum_{k=1}^n k^j$$

for any $j \in \mathbb{N}$, but I feel like this relationship between the sum of the first n cubes and the sum of the first n integers should have some nice geometrical proof. The closest thing I found was the first answer to this question, but I still don't find it intuitively clear. Maybe I am asking for too much here.