Step 1 :The integral of a constant times a function is equal to the constant times the integral of the function.
Step 2 :Therefore, to find the integral of \( \frac{1}{8} x^{3} \) from 4 to 8, we can multiply the given integral of \( x^{3} \) from 4 to 8 by \( \frac{1}{8} \).
Step 3 :Given that the integral of \( x^{3} \) from 4 to 8 is 960, we multiply this by \( \frac{1}{8} \) to get the integral of \( \frac{1}{8} x^{3} \) from 4 to 8.
Step 4 :Doing the multiplication, we get \( 960 \times \frac{1}{8} = 120 \).
Step 5 :Final Answer: The integral of \( \frac{1}{8} x^{3} \) from 4 to 8 is \( \boxed{120} \).