parmenides51 wrote: Prove that for any three distinct positive real numbers $a, b$ and $c$: $$\frac{(a^2 - b^2)3 + (b^2 - c^2)^3 + (c^2 - a^2)^3}{(a - b)^3 + (b - c)^3 + (c - a)^3}> 8abc.$$ Estonia 2009 $$\frac{(a^2- b^2)^3 + (b^2-c^2)^3+(c^2-a^2)^3}{(a- b)^3 + (b-c)^3+(c-a)^3}=(a + b)(b + c)(c + a)> 8abc$$

Small typo in the problem statement.