a^3+3a^2+3a+b^2+3b+2
=a^3+2a^2+a+a^2+2a+1+b^2+2b+1+b
=a(a+1)^2+(a+1)^2+(b+1)^2+b
=(a+1)^2*(a+1)+(b+1)^2+b
=(a+1)^3+(b+1)^2+b