A story which is full of lies. Or a story which starts of true and then gets over exaggerated.
Guy 1: Dude I fucked that hot chick we were talking about last night. You know the one that was across the bar.
Guy 2: Stop telling us this cock story.
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1. A fabricated or highly exaggerated story intended to deceive.
2. A made up story or an exaggerated story, especially if someone sales it as being true.
I don't want to hear another cock and bullshit story about how you don't front.
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It is referred to an untrue or imaginary story
Spare me that cock and bull story, mind you, I can't be easily decieved.