Q:

Can you trap an opponent in a Cube of Force with you?

If you use the fifth face of a Cube of Force in 5E, can you trap the creature inside the cube with you, so he cannot escape (with the exception of DD or teleport)? No living matter, no non-living matter, and no spells can 'pass through' it.
If a silence spell was also cast in that area, could you effectively trap a spell caster inside with you, with no way of escape (unless they have an item they don't need a verbal component to use)?

A:

Yes you can, the walls spring into existence, therefore anything within the cube that's is blocked by the walls is simply stuck inside until the cube is deactivated.
Ref. DMG pp159-160

... Otherwise a barrier of invisible force springs into existence, forming a cube 15 ft on a side.
  The barrier is centered on you, moves with you, and lasts for 1 minute...

