Factorise (p-a)^3 +(p-b)^3 +(p-c)^3 where p=a+b+c/3

Answer 1

So you have
1/27 [ (-2a+b+c)^3 + (a-2b+c)^3 + (a+b-2c)^3 ]
= -1/9 (2a-b-c)(a-2b+c)(a+b-2c)