Intuitive ways to get formula of cubic sum Is there an intuitive way to get cubic sum? From this post: combination of quadratic and cubic series and Wikipedia: Faulhaber formula, I get $$1^3 + 2^3 + \dots + n^3 = \frac{n^2(n+1)^2}{4}$$
I think the cubic sum is squaring the arithmetic sum $$1^3 + 2^3 + \dots + n^3 = (1  + 2 + \dots + n)^2$$
But how to prove it? Please help me. Grazie!

Here are some 'Proof without Words' for this identity;
As Hakim showed (but this one might be slightly clearer);

Here's another very clean illustration by Anders Kaseorg;

Here, the total top volume is undoubtedly $1^2+2^2+3^3+\cdots +n^2,$ while on the volume of the bottom part is;
$$1\left(1+2+\cdots+n\right)+2\left(1+2+\cdots+n\right)+\cdots +n\left(1+2+\cdots+n\right)=\left(1+2+\cdots+n\right)^2.$$
