Let $ P (x) $ and $ Q (x) $ be polynomials with real coefficients such that $ P (0)> 0 $ and all coefficients of the polynomial $ S (x) = P (x) \cdot Q (x) $ are integers. Prove that for any positive $ x $ the inequality holds: $$S ({{x} ^ {2}}) - {{S} ^ {2}} (x) \le \frac {1} {4} ({{P} ^ {2}} ({{ x} ^ {3}}) + Q ({{x} ^ {3}})). $$