$\text{ The sum }\sum _{n=1}^7\frac{\mathrm{n}(\mathrm{n}+1)(2\mathrm{n}+1)}{4}\text{ is equal to }$

$\begin{array}{l}\frac{1}{4}\left[\sum _{n=1}^7\left(2n^3+3n^2+n\right)\right]\\ =\frac{1}{4}\left[2{\left(\frac{7.8}{2}\right)}^2+3\left(\frac{7.8.15}{6}\right)+\frac{7.8}{2}\right]\\ =\frac{1}{4}[2\times 49\times 16+28\times 15+28]\\ =\frac{1}{4}[1568+420+28]=504\end{array}$