[ConfusedHermit (OP)]

I find ocean caves really interesting, but I'm curious about something:
Is it possible for an ocean cave to be completely sealed off and the inside isn't completely full of water?

What about a large rock mass sticking out of the water (but a large interior below) in the middle of the ocean, and the only hole is above the surface of the water so none gets in?

[Bass]

Not likely.  The surrounding rock would have to be impermeable to keep the water out and the air in.

[ConfusedHermit (OP)]

Is that an answer to both of those things?

Also, is it not likely in that it could NEVER happen, or just very very improbable? :{o~

[CliffordK]

I see lots of notes that there are some caves with underwater entrances (either tidally, or 100% of the time), but that may have portions of the cave above sea level, and thus an air pocket can form.

I'm not seeing any confirmation whether or not breathable air pockets in fact exist 100% below the sea level.  Logically, it seems doubtful.  So, for example, if an air pocket was to form at the beginning of the Holocene 10,000 years ago when the sea was rapidly rising, then it would seem like pressure would drive the oxygen and other gases into solution and eventually the air pocket would disappear.

[Mazurka]

Is that an answer to both of those things?

Also, is it not likely in that it could NEVER happen, or just very very improbable? :{o~

Jollyologists seldom commit to anything absolutely - the world keeps on throwing unexpected or paradigm challenging things at them...

However -for the reason CliffordK offers by the mechansim Bass suggests, I would agree with them it is exceptionally unlikely. 

[ConfusedHermit (OP)]

Okay. Thanks to each of you :]

[CliffordK]

I would think that if underwater bubbles of methane can exist from microorganisms decomposing matter, then these bubbles could be directed into a cavern.  Although, it might not be good for humans to breathe.

How deep does one actually get methane bubbles?

I know that algae makes oxygen which gets released into the atmosphere, but I'm having troubles imagining how this could be trapped in a cave.

Most divers exhale lots of air bubbles with concerns that the released air bubbles could accumulate in shipwrecks and presumably also caverns.  The use of a "rebreather" would make it possible to release much less air, and also extend one's air supply.

[syhprum]

I think the most likely gas to accumalate in under sea caverns would be CO2 not very good for breathing.

[damocles]

Blue-green algae photosynthesize and produce oxygen. In order to do so, they need visible light. They can therefore only do so in directly illuminated shallow water. It is indeed difficult to see how oxygen could arrive in an underwater dome structure.

Argon and helium are produced in radioactive decay. These gases can be trapped in particularly impervious underground domes, so no real reason why not in underwater domes. But quantities of these gases would be very small.

Natural gas contains methane and hydrogen and carbon dioxide, and is often associated with oil deposits and trapped in dome structures. I think I have heard that these originate from geological degradation of subducted animal remains, but I am no petroleum geologist.

Methane and carbon dioxide could also come from the anaerobic microbiological degradation of organic detritus on the ocean floor.

Nitrogen, carbon dioxide, and volatile sulfur compounds can be released in undersea volcanic activity, whether eruptions or just vents.

I think that a natural undersea dome filled with a gas mixture is quite a feasible possibility. I cannot see how that gas mixture could be breathable though, or bear more than a distant resemblance to "air:.