sequences and series - 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!

Answer

Maybe this will help you visualize it:

Source.

or this one which is clearer:

$\phantom{XXXXXXXX}$