[a+b+c]^3 – a^3-b^3-c^3.
=a^3 +b^3 +c^3 + 3ab(a + b) + 3bc(b +c) + 3ac(a +c) + 6abc – a^3-b^3-c^3
= 3ab(a + b) + 3bc(b +c) + 3ac(a +c) + 6abc
= 3(ab(a + b) + bc(b +c) + ac(a +c) + 2abc)
= 3(ab(a + b) + b^2c + abc + bc^2 + ac^2 + a^2c + abc)
= 3(ab(a + b) + bc(a + b) + c^2(a + b) + ac(a + b))
= 3(a + b)(c^2 + bc + ab +. ac)
= 3(a + b)(c(b+c) + a(b+c))
= 3(a+ b)(b+c)(c+a)