Question 168
Find the maximal value of the real number $M$ such that for all positive real numbers $a$, $b$, $c$ the following inequality holds:
$$
a^3 + b^3 + c^3 - 3abc \ge M(|a-b|^3 + |b-c|^3 + |c-a|^3)
$$
$$
a^3 + b^3 + c^3 - 3abc \ge M(|a-b|^3 + |b-c|^3 + |c-a|^3)
$$