Factorise

$x^{3}-3 x^{2}+3 x+7$

$=x^{3}-3 x^{2}+3 x+7$

$=x^{3}-3 x^{2}+3 x+8-1=x^{3}-3 x^{2}+3 x-1+8$

$=\left(x^{3}-3 x^{2}+3 x-1\right)+8$

$=(x-1)^{3}+2^{3}$

$=(x-1+2)\left[(x-1)^{2}+4-2(x-1)\right]$

$=(x+1)\left[x^{2}+1-2 x+4-2 x+2\right]$

$=(x+1)\left(x^{2}-4 x+7\right)$