A charge $q$ is placed at the corner of a cube of side $a$. The electric flux passing through the cube is :

According to Gauss's law, the electric flux through a closed surface is equal to $\frac{1}{{\epsilon }_0}$ times the net charge enclosed by the surface.
Since, $q$ is the charge enclosed by the surface, then the electric flux $\varphi =\frac{q}{{\epsilon }_0}$.
If charge $q$ is placed at a corner of cube, it will be divided ito 8 such cubes. Therefore, electric flux through the cube is
${\varphi }^{\prime }=\frac{1}{8}\left(\frac{q}{{\epsilon }_0}\right)$