Take $x=(a+1)(a^3+1),y=a(a+1)(a^3+1)$ for any positive integer $a>1$ Then $\frac{x^2+y^3}{x^3+y^2}=a^3-a+1$ Or $x=a^5-a^2-1, y=ax$ then $\frac{x^2+y^3}{x^3+y^2}=a^3-1$