$$\begin{eqnarray} a(n) &= &1 + 2 + 3 + ... + n \\ b(n) &= &1^2 + 2^2 + 3^2 + ... + n^2\\ c(n) &= &1^3 + 2^3 + 3^3 + ... + n^3. \end{eqnarray}$$
It is well known that $c(n) = a(n)^2$ . What are the relationships between $a(n)$ and $b(n)$ and between $b(n)$ and $c(n)$?