A charge q is placed at corner of a closed cube the flux related with any face of cube.

Charge $=q$

must be $\frac{q}{8{ϵ}_0}$ because cube has $8$ corners hence the charge is partially distributed $\frac{q}{8}$.

Now, using Gauss's law,

the flux $\varphi =\frac{q}{8{ϵ}_0}$

(when ${ϵ}_0=$ permittivity of air $=8.854\times {10}^{-12}F/m$