Find the sum of the following series: `(a-b)^2+(a^2+b^2)+(a+b)^2+...+[(a+b)^2+6a b]`

Explanation

To find the sum of the series given by the expression \((a-b)^2 + (a^2 + b^2) + (a+b)^2 + \ldots + [(a+b)^2 + 6ab]\), we will follow these steps:

### Step 1: Identify the terms in the series
The series consists of the following terms:
1. \( (a-b)^2 \)
2. \( a^2 + b^2 \)
3. \( (a+b)^2 \)
4. Continuing until the last term \( (a+b)^2 + 6ab \)
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