The problem requires evaluating the numerical expression $[8 \div (7+1)]^3$.

1. Problem Description

The problem requires evaluating the numerical expression $[8 \div (7+1)]^3$.

2. Solution Steps

First, we need to evaluate the expression inside the parentheses:

$7 + 1 = 8$

Next, we substitute this result back into the expression inside the brackets:

$8 \div 8 = 1$

Finally, we raise this result to the power of 3:

$1^3 = 1 \times 1 \times 1 = 1$

3. Final Answer

1