1. **State the problem:** We are given two functions $f(x) = 3x - 8$ and $g(x) = x^3$. We need to find an expression for the composite function $g(f(x))$. 2. **Recall the definition of composite functions:** The composite function $g(f(x))$ means we substitute $f(x)$ into $g(x)$. In other words, wherever there is an $x$ in $g(x)$, replace it with $f(x)$. 3. **Write the formula:** $$g(f(x)) = (f(x))^3$$ 4. **Substitute $f(x)$ into $g(x)$:** $$g(f(x)) = (3x - 8)^3$$ 5. **Explain the expression:** This means the output of $f(x)$ is raised to the third power in $g(f(x))$. The expression $(3x - 8)^3$ is the cube of the binomial $3x - 8$. 6. **Final answer:** $$\boxed{g(f(x)) = (3x - 8)^3}$$ This is the expression for the composite function $g(f(x))$.