To find \( f(3) \) using the function rule \( f(x) = 8^x - 6 \), we substitute \( x = 3 \) into the function:
\[ f(3) = 8^3 - 6 \]
First, we calculate \( 8^3 \):
\[ 8^3 = 8 \times 8 \times 8 = 64 \times 8 = 512 \]
Now, we substitute this back into the equation:
\[ f(3) = 512 - 6 \]
Now, perform the subtraction:
\[ f(3) = 506 \]
Thus, the final answer is:
\[ f(3) = 506 \]