Question

The mean of cubes of first $15$ natural numbers is _____.

• A. $980$
• B. $960$
• C. $1920$
• D. $1940$

Answer 1

The correct option is B $960$

Sum of cubes of first $n^2$ numbers $={\frac{n(n+1)}{2}}^4$
So, sum of cubes of first $15$ numbers $={\frac{{15}^2(15+1)}{4}}^2=\frac{225\times 256}{4}=14,400$
And mean of the cubes of first $15$ numbers $=\frac{\text{Sum of cubes of first}15\text{numbers}}{15}=\frac{14,400}{15}=960$