Find the value

Taking $x$ common in $x^{3}+x$

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

Taking $-3$ common in $-3 x^{2}-3$

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

Now, we take $\left(x^{2}+1\right)$ common

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

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