JBMO-SL 2014 A2

Let $a, b$ and $c$ be positive real numbers such that abc $=\frac{1}{8}$. Prove the inequality

$$a^{2}+b^{2}+c^{2}+a^{2} b^{2}+b^{2} c^{2}+c^{2} a^{2} \geq \frac{15}{16}$$

When does equality hold?