Find the sum using the formulas for the sums of powers of integers.
$$\sum _ { n = 1 } ^ { 12 } n ^ { 3 }$$
A) 4356
B) 12,168
C) 1728
D) 650
E) 6084

Question

Quizplus · Accepted Answer

The formula for the sum of cubes of the first $n$ natural numbers is $\left( \dfrac{n(n+1)}{2} ight) ^2$. Plugging in $n=12$ gives $\left( \dfrac{12(13)}{2} ight) ^2 = 6084$. Therefore, the answer is $\boxed{	extbf{(E) }6084}$.

Find the Sum Using the Formulas for the Sums of Powers