I recently proved that

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

using mathematical induction. I’m interested if there’s an intuitive explanation, or even a combinatorial interpretation of this property. I would also like to see any other proofs.

**Answer**

Stare at the following image, taken from this MO answer, long enough:

**Attribution***Source : Link , Question Author : Fernando Martin , Answer Author : Parcly Taxel*