Answer
Not correct factorization
Correct: $(x+2)(x^2+x+1)$
Work Step by Step
We graph the polynomial functions:
$$\begin{align*}
p_1(x)&=(x+1)^3+1\\
p_2(x)&=(x+1)(x^2+x+1).
\end{align*}$$
Because the two graphs do not coincide, this means that the polynomial $p_1(x)=(x+1)^3+1$ was not factored correctly.
Factor the polynomial $p_1(x)$ correctly:
$$\begin{align*}
p_1(x)&=(x+1)^3+1\\
&=((x+1)+1)((x+1)^2-(x+1)+1)\\
&=(x+2)(x^2+2x+1-x-1+1)\\
&=(x+2)(x^2+x+1).
\end{align*}$$
We draw $p_2(x)=(x+2)(x^2+x+1)$ and notice that now the two graphs coincide.