The white ones you see during the day are Cabbage White BUTTERFLIES. Their caterpillars are solid fuzzy green. There are also a couple of moths that lay eggs on your cabbages during the night. Their caterpillars have black markings on them or are a looper-type (inchworm) solid green. Single most effective method, since cabbage is a leaf-crop, is to cover them with netting like tulle or spun-bonded fabric supported in some way to keep the fabric from touching the leaves.
If you don't have many, you can inspect each leaf top and bottom for eggs. A small hole and tiny frass (poop) can help you detect the newly hatched caterpillars.
On the other hand, if you don't have your cabbages covered, you'll see wasps and hornets patrolling and inspecting EVERY SINGLE LEAF. Even the ones that you can't get to and down into the gaps where the leaves connect to the stem. They feed the caterpillars to their young.
So far, the baby caterpillar has been missing from the leaves with hatchling holes that I've turned over.