Calculus (3rd Edition)

Expanding $(2j+1)^{2}$ and using formulas (3) and (4), we get $$\sum_{j=1}^{30}(2j+1)^{2}=\sum_{j=1}^{30}(4j^{2}+4j+1)$$$$=4\sum_{j=1}^{30}j^{2}+4\sum_{j=1}^{30}j+\sum_{j=1}^{30}1$$$$=4\times\frac{30(30+1)(2\times30+1)}{6}+4\times\frac{30(30+1)}{2}+1(30-1+1)=37820+1860+30=39710$$