The problem asks to evaluate the series $\sum_{n=4}^{6} (n^2 - 1)$. This means we need to sum the expression $n^2 - 1$ for $n = 4, 5, 6$.

1. Problem Description

The problem asks to evaluate the series $\sum_{n=4}^{6} (n^2 - 1)$. This means we need to sum the expression $n^2 - 1$ for $n = 4, 5, 6$.

2. Solution Steps

First, we evaluate the expression $n^2 - 1$ for each value of $n$ from 4 to

6.

For $n = 4$:

$4^2 - 1 = 16 - 1 = 15$

For $n = 5$:

$5^2 - 1 = 25 - 1 = 24$

For $n = 6$:

$6^2 - 1 = 36 - 1 = 35$

Now, we sum these results:

$15 + 24 + 35 = 74$

3. Final Answer

The final answer is 74.