$\begin{array}{ccc}{1}^3+2^3+3^3+...+n^3\hfill & =\hfill & (1+2+3+...+n){}^2\hfill \\ \multicolumn{0}{c}{}& =\hfill & {\left(\frac{n(n+1)}{2}\right)}^2\hfill \\ \multicolumn{0}{c}{}& =\hfill & \frac{n^4+2n^3+n^2}{4}\hfill \\ \multicolumn{0}{c}{}\end{array}$