Find the magnetic flux through each of the faces of the cube and what is the total magnetic flux through cube?

Just multiply the field strength by the projected area that is perpendicular to the field. The field enters through two sides which are oriented at 45 deg to the field, and exits through the opposite two sides.
Say the diagonal is from upper right to lower left and the field is directed that way. Then the two entry sides are the top and right faces, and the exit sides are the bottom and left faces. There is no flux through the front and rear faces. The projected area of the sides the flux passes through is 0.5*1*sqrt(0.5) = 0.353553 m^2, so the flux = 0.45*0.353553 = 0.237171 Wb.