Is the binding energy made up of gluons?
Sure you can describe the electric field in that case by a viewpoint where you sum virtual photons together to get said electric field. Whereas a non virtual photon is alltogether a different thing. You can actually describe a normal non virtual photon as a sum of virtual photons.
Point is that virtual particles are just a mathematical tool.
Actual real gluons do exist and they're analogous to the actual photon.
In case of electromagnetism the actual stuff is the electric field. With proton (so in quantum chromodynamics) it's the gluon field. It's called that because every particle has a field and every field a particle. It would be kinda like calling electric field a photon field. Same difference.
To think of a proton as containing tons of gluons would be a mistake.
Additionally gluons are expected to be massless, they basically come into existence as needed.
In a charged capacitor, there's a lot of electrons on one side, but very few of them on the other. When you close the capacitor, suddenly you get a lot of energy out of it.
It's not exactly informative nor true. Yes you can describe the electric field as sum of virtual photons but that's different to a normal photon. And even then the electric field is not the same as the potential energy. Sure it defines it but it's not the same as the potential energy of the charged object.
In case of protons it's the same. It's better to think of it as a field, which it is. Gluon in itself is "just" an excitation of that field. Just like photon is an excitation of the electric field. And the binding energy of the proton comes from the quarks interacting with the gluon field.
The reason I'm talking so much against the virtual particle viewpoint because then people will start thinking of some things whizzing about. That's not what happens. It's a field.
It's actually better to think of even the normal fermions with mass with fields, because that's what they are. It's no longer surprising that how does electron go through both slits at the same time or how all electrons are identical. Of course they are identical as there is just one electron field that has a very specific kind of excitation that propagates.
This is not some random "Look at my weird theory". It's what Quantum Field Theories are. I mostly blame bad science journalism looking at Feynman diagrams (a great mathematical tool, don't get me wrong) that has people thinking too much about virtual particles.