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