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

s_n 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,

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

s_n denotes the sum of the first n natural numbers.

To determine the given ratio in the question,

₌

So, the value of