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.
The big cock on the farm was a bit of a troublemaker. It liked to tease the farm dog by running close to it and then quickly running away. One day, it learned its lesson when the dog chased it up a tree.
On a particular farm, there was a first big cock that had an interesting story. This cock was not only large in size but also had a unique personality. It was the first to explore new areas of the farm. Once, it led the other chickens to a new patch of grass that they hadn't discovered before. It was very territorial and would fight off any other cocks that tried to invade its space. The hens seemed to be attracted to it because of its confidence and size.
One story could be that a wife on a small farm had a big rooster. The rooster was very protective of the hens. It would crow every morning to wake the wife up, and she grew quite fond of it. It became a part of the daily life on the farm.
One story could be a girl was very scared at first when she saw a big rooster in the farm. But then she learned to feed it and became friends with it. She was initially afraid of its large size and loud crowing, but over time, she found it interesting to watch it strut around.
Male turkeys also have an interesting growth pattern. Their snoods (the long, fleshy growths on their heads) and their tail feathers grow as they age. The more prominent these features are, the more likely the male turkey is to attract a female. The growth of these features is part of the male turkey's development into a sexually mature and attractive individual.
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.