Answer
$(y+2)(y^{2}+y+1)$
Work Step by Step
$(y+1)^{3}+1=\quad$ ... recognize a sum of cubes
$=(y+1)^{3}+1^{3}\quad$... apply $A^{3}+B^{3}=(A+B)(A^{2}-AB+B^{2})$
$=[(y+1)+1][(y+1)^{2}-(y+1)+1]$
$\quad$... apply $(A+B)^{2}A^{2}+2AB+B^{2}$
$=(y+2)[(y^{2}+2y+1)-y-1+1]$
$=(y+2)(y^{2}+2y+1-y-1+1)$
= $(y+2)(y^{2}+y+1)$
