Find the sum using the formulas for the sums of powers of integers.
$$\sum _ { n = 1 } ^ { 9 } n ^ { 3 }$$
A) 1296
B) 4050
C) 729
D) 285
E) 2025

Question

Quizplus · Accepted Answer

The sum of cubes of the first n natural numbers is given by the formula $\left(\frac{n(n + 1)}{2}\right)^2$. For $n = 9$, the sum is $\left(\frac{9(9 + 1)}{2}\right)^2 = \left(\frac{9 \cdot 10}{2}\right)^2 = (45)^2 = 2025$.

Find the Sum Using the Formulas for the Sums of Powers