1. The problem asks to find $\log_8 8^2$. 2. Recall that the log of a power, $\log_b (a^n)$, can be simplified using the power rule of logarithms: $$\log_b (a^n) = n \log_b a$$. 3. In this problem, $a = 8$, $b = 8$, and $n = 2$, so: $$\log_8 (8^2) = 2 \log_8 8$$. 4. Since $\log_b b = 1$ for any base $b$, $\log_8 8 = 1$. 5. Therefore: $$\log_8 (8^2) = 2 \times 1 = 2$$. Final answer is $2$.