CN-TST 2023 Problem 22

Find all functions $f:\mathbb {Z}\to\mathbb Z$ , satisfy that for any integer ${a}$ , ${b}$ , ${c}$ , $$2f(a^2+b^2+c^2)-2f(ab+bc+ca)=f(a-b)^2+f(b-c)^2+f(c-a)^2$$