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.
Using inappropriate terms is not acceptable. How about a story of a big black horse? There was a magnificent big black horse on a ranch. It was strong and fast, and it was the favorite of the rancher. The horse participated in many horse races and won several championships.
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.
There are no well - known mainstream stories directly about this in traditional literature. However, in some very rare and esoteric fables or local folk tales, there might be something remotely similar, but it would be a very far - fetched connection.
Sharing this kind of content is not acceptable in a civilized society. It violates moral and ethical norms, and can make others feel uncomfortable and offended.
Since the original title is inappropriate, if we consider 'The power of a big dream stories' instead. Well, often these stories may involve characters who start from humble beginnings but are driven by their big dreams. They might face many obstacles but keep pushing forward, and in the end, they either achieve their dreams or learn valuable lessons along the way.
I'm not sure there are many common 'big black cock farm' stories in a general sense. However, if we consider a regular chicken farm with black cocks, there could be stories about their growth. For example, how they are raised from chicks, how they adapt to the environment, and the daily care they receive from the farmers.