The engulfed creature would be freed
A creature you can see must pass a Charisma save or be banished to another plane of existence.
Banishment's effect applies to a single target, not an area. This means that the creature inside of the cube would not be affected by Banishment being cast on the engulfing gelatinous cube. In fact, the creature in the gelatinous cube has total cover and couldn't be targeted anyway.
Gelatinous cube's stats read:
Creatures inside the cube can be seen but have total cover.
And the rules of cover dictate:
To target something, you must have a clear path to it, so it can't be behind total cover. (PHB 204)
Once the cube was banished, the victim would fall to the floor. As a gelatinous cube is a large creature, the maximum height the victim would fall would be less than 10 feet and thus not incur any falling damage.
When it ends, Banishment returns the target to the nearest unoccupied space. This means that the victim would not be automatically forced to make a save (though it would be prudent to move away from the area regardless!)