Listening to the Dan Patrick Show this morning on radio, I heard one of his guests quote the phrase cock strong to mean a person with strength of purpose. The guess deliberately disabused the notion that the cock being referred to was part of the human anatomy. Instead, as Patrick chimed it, it referred to the rooster, and it was "farm talk."
However, I couldn’t find the phrase in the dictionary, but Urban Dictionary had this to say:
A guy with a wandering/lazy eye. His eye is weighed down due to the size of his johnson.
Man: "That dude has got a messed-up eye."
Girl: "No, he’s just cock strong, trust me!"
I could see the phrase’s being defined either way. If anyone has any information on its usage or derivation, please leave a comment.