Is empty space made of energy? GR says that matter bends space around it, QM says even empty space must contain something. Is empty space a form of energy?
 A: I think there are two different questions here.
The first question is "what is spacetime?". This is well covered by the answers to the question Is space-time a special form of energy? and there's no need to go into this again. Suffice to say that spacetime is a mathematical object not a physical obect so isn't made of anything.
The other question is what effect vacuum energy has on spacetime, and this is an area we really don't understand yet.
Vacuum energy should behave like a cosmological constant or dark energy. It behaves as if it has a negative pressure and it should be causing the expansion of the universe to accelerate. You may have heard that dark energy is indeed making the expansion accelerate, but the trouble is that a naive calculation suggests vacuum energy should make the expansion accelerate much, much faster that we observe. So fast in fact that stars wouldn't have had time to form before the expansion diluted all the matter to effectively zero.
And that is a problem because vacuum energy is certainly real, as the Casimir effect shows, but it doesn't appear to affect spacetime in the way we expect. The explanation for this is currently unknown.
