>>475
x^3 + y^3 = (x+y)(x^2 -xy+y^2)

(a-b)^3 +(b-c)^3 = (a-c){ (a-b)^2 -(a-b)(b-c)+(b-c)^2}
(a-b)^3 +(b-c)^3 +(c-a)^2 = (a-c){ (a-b)^2 -(a-b)(b-c)+(b-c)^2} +(c-a)^3
=(a-c){ (a-b)^2 -(a-b)(b-c)+(b-c)^2 -(c-a)^2}
=(a-c){ (a-b)^2 -(a-b)(b-c)+(b-c)^2 -(c-a)^2}
=(a-c){ (a-b){(a-b) -(b-c)} + {(b-c)+(c-a)} {(b-c)-(c-a)} }
=(a-c){ (a-b)(a-2b+c) +(b-a)(a+b-2c)}
=(a-c) (a-b){ (a-2b+c) - (a+b-2c)}
=(a-c)(a-b)(-3b+3c)
=3(c-a)(a-b)(b-c)