a^3+3a^2+3a+2

=(a^3+2a^2+a)+a^2+2a+2

=a(a+1)^2+(a+1)^2+1

=(a+1)^3+1

=(a+2)[(a+1)^2-(a+1)+1]

=(a+2)(a^2+2a+1- a-1+1)

=(a+2)(a^2+a+1)