Find the sum to n terms of the series :`1^2+(1^2+2^2)+(1^2+2^2+3^2)+dotdotdot`

Explanation

To find the sum to n terms of the series \( S_n = 1^2 + (1^2 + 2^2) + (1^2 + 2^2 + 3^2) + \ldots + (1^2 + 2^2 + \ldots + n^2) \), we can follow these steps:

### Step 1: Understand the series structure
The series can be represented as:
\[ S_n = \sum_{k=1}^{n} \sum_{j=1}^{k} j^2 \]
This means we are summing the squares of the first \( k \) natural numbers for each \( k \) from 1 to \( n \).
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