I know that $1+2+\dots+n=\dfrac{n(n+1)}{2}$ and $1^3+2^3+\dots+n^3=\dfrac{n^2(n+1)^2}{4}$ and can show by algebraic calculation. But I am wondering if there is any logical argument or any intuitive argument to show that:
$(1+2+\dots+n)^2=1^3+2^3+\dots+n^3$
Thanks.