IT-CESENATICO 2023 Problem 5

Let $a, b, c$ be reals satisfying $a^2+b^2+c^2=6$ . Find the maximal values of the expressions a) $(a-b)^2+(b-c)^2+(c-a)^2$ ; b) $(a-b)^2 \cdot (b-c)^2 \cdot (c-a)^2$ . In both cases, describe all triples for which equality holds.