Problem

Source: SRMC 2007

Tags: inequalities, inequalities proposed



Find the max. value of $ M$,such that for all $ a,b,c>0$: $ a^{3}+b^{3}+c^{3}-3abc\geq M(|a-b|^{3}+|a-c|^{3}+|c-b|^{3})$