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The sum, $\sum_{n=1}^{7}\frac{n(n+1)(2n+1)}{4}$ is equal to _______.
$= \frac{1}{4} \cdot \frac{7}{8}\sum_{n=1}^{7}(2n^3 + 3n^2 + n)$
$= \frac{1}{4}\left[2\left(\frac{7.8}{2}\right)^2 + 3\left(\frac{7.8.15}{6}\right) + \frac{7.8}{2}\right]$
$\Rightarrow \frac{1}{4}[1568 + 420 + 28] = \frac{1}{4}[2016] = 504$
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