This is the explanation:
The three faces which are nearer to the charge are symmetrical to each other.
Similarly the three faces which are further away from the charge are symmetrical to one another.
So the combination of one near face and the corresponding opposite further face is symmetrical with the other two combinations.
Now flux thru cube = qεo
So flux thru each combination of near face and opposite face = (1/3)qεo
= q3εo