I don't know if I could cull the Cockerels or even know how, but I will say, we raised a batch of chicks and four out of nine were Cockerels. We let them hatch naturally, and one of my favorite chickens were their mother hen. We thought how cool is this and aren't they adorable and so cute with the mom.
But as they got older, and mind, we already had a couple of roosters, the young Cockerels started jumping on the hens, especially poor mom. And sometimes all three boys at a time, taking turns. They were really hot to trot.
So I am sad to say, keeping those Cockerels around cost me the life of the mother hen and another favorite hen, before I realized what was happening. I was a fairly new chicken owner, and didn't have a clue. Those hens probably, literally had their eggs scrambled inside of them. Then they got infections and died.