Kocken is because it is The cook. En Kock would have been used if it was A cook.
I have two ways to post it: En kock dricker kaffe, och Kocken dricker kaffe
En kock dricker kaffe = A cook drinks coffee
Kocken dricker kaffe = The cook drinks coffee
Kocken dricker kaffe
Why not "kockan"?
Do you mean the female form "en kocka - kockan"? I'd say it's never used nowadays.
Cooking with Kock