BALKAN 2015 Problem 1

Let $a, b$ and $c$ be positive real numbers. Prove that

$$a^{3} b^{6}+b^{3} c^{6}+c^{3} a^{6}+3 a^{3} b^{3} c^{3} \geq a b c\left(a^{3} b^{3}+b^{3} c^{3}+c^{3} a^{3}\right)+a^{2} b^{2} c^{2}\left(a^{3}+b^{3}+c^{3}\right)$$