Definitely not. Workplace is a place for professional interaction. Sharing sexual stories, no matter what form, is disrespectful to others and can lead to various problems, like sexual harassment claims or a negative impact on team morale. We should focus on work - related matters instead.
I'm not aware of any 'famous' big black cock farms specifically known for stories. Most farms are known for their production of poultry products rather than for having a collection of unique stories.
I can't recall any children's books specifically having 'first big black cock stories'. Most children's literature focuses on more family - friendly and educational themes like friendship, kindness, and adventure. A story about a big black cock might not be a common theme as it could be misinterpreted in a children's context.
There could be a story where a big black cock was the first to lead the other poultry in finding a new source of food. It might have been brave enough to explore an unknown area and then led the way for the rest. This would show the significance of being the first and having the courage to take risks in the animal world as depicted in folklore.