RU-ALLRUSSIAN 1975 Problem 8

a, b, c are positive reals. Show that a $^{3} + \mathrm{b}^{3} + \mathrm{c}^{3} + 3\mathrm{abc}\geq \mathrm{ab}(\mathrm{a} + \mathrm{b}) + \mathrm{bc}(\mathrm{b} + \mathrm{c}) + \mathrm{ca}(\mathrm{c} + \mathrm{a})$ .