Several beekeepers with foundationless frames have reported finding large number of drone cells in their hives. In some cases, the new brood is 25% to 50% drones.
While colonies on foundationless frames always have more drones than those on preformed foundation, the number of drones can seem out of hand. And indeed, vast amounts of hive resources are going to raising these bees who give nothing in return. Instead of having workers out there collecting honey and raising more workers, you have hundreds of drones lazing around, waiting to be fed.
The first thing you should do is make sure the queen is laying at least some worker brood. If so, the queen is probably fine. If you see no worker brood—or at least none in a clear pattern—you may have an infertile queen that needs to be replaced. Although not frequent, it does happen from time to time.
If you think the queen is okay, you can try moving the drone brood to the outside of the brood nest and inserting new frames near the center of the nest. It is usually best not to remove the drone frames completely (unless you are doing it for mite control) because the colony will just expend more energy in an effort to replace it.
One thing to remember is that most drone brood is raised in early spring just before and during swarm season. It should taper off after that. You may just have to be patient for a few weeks. As the season progresses you should see a greater and greater percentage of worker brood.
Some beekeepers use a queen excluder just about the hive entrance to keep the drones from returning to the hive where they take up space and use resources. The problem with this is that newly hatching drones are unable to leave, so it is necessary to remove the queen excluder every few days to allow the newly-hatched drones to exit.
Another thing you can try is using a pre-stamped piece of wax foundation as a starter strip to encourage worker-sized cells. If you have a proper saw, you can even cut starter strips from plastic foundation.
Remember, there are many reasons that beekeepers developed pre-stamped foundation. One of them was to keep down the number of drones. If you go foundationless, you will always be faced with a higher proportion of drones and a lower yield of honey than a beekeeper using patterned foundation. Every method has its pros and cons.