Find the sum of `n` terms of the series `1.3.5.+3.5..7+5.7.9+...`

Explanation

To find the sum of the series \( S_n = 1 \cdot 3 \cdot 5 + 3 \cdot 5 \cdot 7 + 5 \cdot 7 \cdot 9 + \ldots \) up to \( n \) terms, we will first identify the general term of the series and then derive the sum.

### Step 1: Identify the General Term
The series consists of products of three consecutive odd numbers. The first term is \( 1 \cdot 3 \cdot 5 \), the second term is \( 3 \cdot 5 \cdot 7 \), and the third term is \( 5 \cdot 7 \cdot 9 \).

We can express the general term \( T_n \) as:
\[
T_n = (2n - 1)(2n + 1)(2n + 3)
...