KöMaL 2012 A561

Show that $\frac{a^3b}{{(3a+b)}^p} + \frac{b^3c}{{(3b+c)}^p} +\frac{c^3a}{{(3c+a)}^p} \ge \frac{a^2bc}{{(2a+b+c)}^p} + \frac{b^2ca}{{(2b+c+a)}^p} + \frac{c^2ab}{{(2c+a+b)}^p}$ holds for all positive numbers $a$, $b$, $c$, $p$.