Question

The sum of the cubes of three consecutive natural numbers is divisible by

• A. 7
• B. 9
• C. 25
• D. 26

Answer 1

The correct option is B 9

Let $P\left(n\right)=$ sum of cube of three consecutive natural numbers
$\Rightarrow P\left(n\right)=n^3+(n+1{)}^3+(n+2{)}^3$
Now, $P\left(1\right)=1+8+27=36$ divisible by only $9$ from the given option
Hence only option 'B' is correct choice.