Step 1 :Given functions are \(f(x)=x^{3}\) and \(g(x)=|x+1|\).
Step 2 :We need to find \(f(g(x))\).
Step 3 :Substitute \(g(x)\) into \(f(x)\) to get \(f(g(x)) = (|x+1|)^3\).
Step 4 :So, the final answer is \(f(g(x)) = \boxed{(|x+1|)^3}\).