We have :

\(\dfrac{n^3}{3}+\dfrac{n^3}{2}+\dfrac{n^3}{6}=\dfrac{2n^3}{6}+\dfrac{3n^3}{6}+\dfrac{n^3}{6}\)

\(=\dfrac{2n^3+3n^3+n^3}{6}=\dfrac{6n^3}{6}=n^3\)

So, we have the thing to prove :)