If Sn denotes the sum of the cubes of the first n natural numbers and sn denotes the sum of the first n natural numbers then find the value of .

Given in the question, Sn denotes the sum of the cubes of the first n natural numbers.


sn denotes the sum of the first n natural numbers.


Note:


I. Sum of first n natural numbers, 1 + 2 +3+…n,



II. Sum of squares of first n natural numbers, 12 + 22 + 32+….n2,



III. Sum of cubes of first n natural numbers, 13 + 23 + 33 +…..n3,



IV. Sum of a constant k, N times,



So,


Sn denotes the sum of the cubes of the first n natural numbers. (Given data in the question).



sn denotes the sum of the first n natural numbers.




To determine the given ratio in the question,







=


So, the value of


1