UPSC CDS 2 2018 Math Paper

Let the three consecutive natural numbers be (x – 1), x and (x + 1).
Then, (x−1)2+x2+(x+1)2=110
⇒3x2=108⇒x2=36⇒x=6
Since natural numbers are positive integers, therefore, we cannot consider x = –6.
Other numbers are (x – 1), i.e., 5 and (x + 1), i.e., 7.
Sum of cubes of numbers=53+63+73=684