It's all a question of usage:
I like cabbage -- this is probably the most common way of saying this. (non-count usage)
I like cabbages -- this strikes me as a little odd. But it is possible, especially if you're referring to different types of cabbage. (I like red cabbage, and I like green cabbage, so I like cabbages). (count usage)
I like a cabbage -- can be used in colloquial English, but it would usually be followed by something, for example "I like a cabbage from time to time."
The problem arises because it's not clear if cabbage is a count noun or a noun count noun. It can be thought of both ways.
If non count, then "I like cabbage" would be more ordinary. And if you bought one, you would say, "I bought a head of cabbage". (non count usage)
If count, then "I like cabbages" is fine, and when you go to the store, you buy a cabbage. (count usage)
"I like a cabbage" is colloquial, like "I like a good coffee from time to time." or "I like a good wine from time to time."