Solving $T(n) = 4T(n/2) + n^3$ with substituton method
Your guess works: if $T(n) \le c n^3$ and $c \ge 2$ then
$$
T(n) = 4c \frac{n^3}{8} + n^3 = \frac{c}{2} n^3 + n^3 = cn^3 \left(\frac{1}{2}+\frac{1}{c} \right) \le cn^3.
$$