(a+b+c)^3

=(a^2+b^2+c^2+2ab+2bc+2ac)(a+b+c)

=a^3+ab^2+ac^2+2a^2b+2abc+2a^2c+a^2b+b^3+bc^2+2ab^2+2b^2c+2abc+a^2c+b^2c+c^3+2abc+2bc^2+2ac^2

=a^3+b^3+c^3+3ab^2+3a^2b+3a^2c+3ac^2+3bc^2+3b^2c+6abc