Most professionals in the industry would advise you to write only the first book in the series, or maybe the first two, then perhaps leave the others in outline or synopsis stage. The problem is that if you don’t sell the first one, you may not be able to sell any of the others unless they can stand alone or somehow be separated from this series.

In any case, the answer to your question on how to present your series is to query the first book, and mention it’s the first in a planned series. I’d recommend you don’t say a series of “six” because the magic number is often three, and six may scare away some agents and editors. It might lead them to think you have unrealistic expectations and don’t understand how publishing works.

You need to sell the agent on one book. Sometimes a first-time author will get a contract for a three-book deal if the series is strong, so you definitely want to mention it’s a series, but the method is always the same: sell them on that first book.

If you find you’re not able to sell that one, maybe you can pick another in the series that’s stronger in plot or voice or interest; you can start trying to sell that one as the “first” in the series. I’ve had a couple of authors who got 3-book deals this way.

I highly recommend you stop writing this series, at least until you start getting some feedback on whether or not you’re in the ballpark of being saleable. It sounds like you’re on a roll, and you’re enjoying it, and I would assume your writing is getting better and better with each book. But you want to guard against two things: (1) Spending too much time on a series that you don’t know yet whether you can sell; and (2) Getting so comfortable with this set of characters and this storyline that you’re paralyzed when it comes to writing anything else. You may be too invested in this series.

I recommend you start querying, and meanwhile, work on a new book or series, something that doesn’t depend on all these other books selling. Hope that helps!