JBMO-SL 2012 A2

Let $a, b, c$ be positive real numbers such that abc $=1$. Show that

$$\frac{1}{a^{3}+b c}+\frac{1}{b^{3}+c a}+\frac{1}{c^{3}+a b} \leq \frac{(a b+b c+c a)^{2}}{6}$$

so