Let $ a,b$ and $ c$ be positive real numbers. Prove that $ $ \sum_{cyc} \frac {a^3b}{(3a+2b)^3} \ge \sum_{cyc} \frac {a^2bc}{(2a+2b+c)^3} $ $

This problem is from Iran 3rd round-2017-Algebra final exam-P3,Now I can’t find this inequality have solve it,maybe it seem can use integral to solve it?