Let $a,b,c \in \mathbb{R}$. Prove that $$\sum_{cyc} (a^3-b^3)^2+3\sum_{cyc}(a^2-b^2)^2+6(a-b)(b-c)(c-a)(ab+ bc+ca) \ge 0.$$ (LightLucifer)
Problem
Source: Mathcenter Contest / Oly - Thai Forum 2011 (R1) p1 sl-1 https://artofproblemsolving.com/community/c3196914_mathcenter_contest
Tags: inequalities, algebra