Find the sum of first `n` terms of the series `1^3+3xx2^2+3^3+3xx4^2+5^3+3xx6^2+ w h e n` `n` is even `n` is odd

Explanation

To find the sum of the first `n` terms of the series \(1^3 + 3 \times 2^2 + 3^3 + 3 \times 4^2 + 5^3 + 3 \times 6^2 + \ldots\), we will analyze the series separately for the cases when `n` is even and when `n` is odd.

### Step-by-Step Solution:

#### Case 1: When `n` is even

1. **Let \( n = 2m \)**: Since `n` is even, we can express it as \( n = 2m \) where \( m \) is a positive integer.

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