In the end of the loop, if I understand correctly, you have: $\begin{align*}s&=\sum_{i=0}^b \left(\frac{(4i+4)^3+5(4i+4)}{3}+2\right)=\sum_{i=0}^b \left(4\frac{16i^3+48i^2+53i+21}{3}+2\right)\\&=\frac{64}{3}\sum_{i=0}^b i^3+64\sum_{i=0}^b i^2+\frac{212}{3}\sum_{i=0}^b i+30\sum_{i=0}^b 1 \end{align*}$ Using the formulas (which you can prove by induction, if you want): $\sum_{i=0}^b 1=b+1, \hspace{10pt} \sum_{i=0}^b i=\frac{b(b+1)}{2}, \hspace{10pt} \sum_{i=0}^b i^2=\frac{b(b+1)(2b+1)}{6}, \hspace{10pt} \sum_{i=0}^b i^3=\frac{b^2(b+1)^2}{4}$ You can get: $\begin{align*}s&=\frac{64}{3}\frac{b^2(b+1)^2}{4}+64\frac{b(b+1)(2b+1)}{6}+\frac{212}{3}\frac{b(b+1)}{2}+30(b+1)\\&=\frac{16}3 b^4+32 b^3+\frac{218}3 b^2+76 b+30=\frac23(b+1)(8 b^3+40 b^2+69 b+45)\end{align*}$