How to calculate electric flux through a cube of side A, due to a point charge 'q' kept at one of its vertices?
For such type of Question you should know few concept of Solid state...
A spherical body kept at the corner of CUBE contribute 1/8 of its part inside the cube and 7/8 part outside.
A spherical body kept at the edge of CUBE contribute 1/4 of its part inside and 3/4 out side...
A spherical body kept at the center of CUBE contribute its whole part inside the cube.
A spherical body kept at the Faces contribute 1/2 of its part inside the cube.
Now for your Case when charge is kept at the corner...Then total flux through the cube will be only due to q/8 ...
So Flux is equal to q/8epsilon