a^3+3a^2+3a+b^3+3b^2+3b+2
=(a^3+3a^2+3a+1)+(b^3+3b^2+3b+1)
=(a+1)^3+(b+1)^3
=[(a+1)+(b+1)][(a+1)^2-(a+1)(b+1)+(b+1)^2]
=(a+b+2)(a^2-ab+b^2+a+b+1)