I have the following summation: $\sum_{i=0}^n\left(6in + n(8n+2)\right).$ Evaluating I get \begin{align*} 6n\left(\frac{n(n+1)}{2}\right) + n(8n+2) = 3n(n(n+1)) + n(8n+2)\\ &=3n^2(n+1) + n(8n+2)\\ &=3n^3 + 3n^2 + 8n^2 + 2n\\ &=3n^3 + 11n^2 + 2n. \end{align*}
Is this correct?