There can't be a positive interpretation for this. It involves disrespect towards different races and inappropriate sexual implications. In a diverse and inclusive society, we should avoid any form of such offensive expressions.
Most literature focuses on positive, inclusive and respectful themes. Themes like this are often not part of the acceptable or recognized body of work as they can be seen as offensive and discriminatory, so it's difficult to name any relevant stories.
These stories have negative implications. They can promote stereotypes and fetishization. It objectifies people based on race and sexual orientation, which is not acceptable in a diverse and inclusive society.
I'm not sure there are many common or traditional stories specifically about this in a family context. It could potentially refer to a situation where a black rooster is part of a white - family - run poultry farm. In some rural areas, families of any ethnicity might keep different breeds of poultry for various reasons like eggs and meat production.
Movies usually approach interracial relationships in a more positive and respectful way. There are films that explore the connection between a black man and a white woman, but not in the offensive way the title implies. One such example could be 'Jungle Fever' which delves into the complex relationship between the two characters from different races, dealing with issues like family reactions, cultural differences, and the power of love.
The term is rather ambiguous. It might be a very specific set of stories known only within a certain group. It could be stories that involve a white doctor and something related to black cocks in a symbolic or literal sense. For example, if it's in a symbolic sense, perhaps the black cocks represent something unique in the story, like a symbol of strength or a cultural totem, and the white doctor has some sort of interaction with it or related to it.
It could be a story of redemption. The white boy might be in prison for some minor offense and the black man, who has been there for a long time, teaches him about life. The 'big black prison' could symbolize a place of transformation. The black man could share his experiences of racial discrimination within the prison walls, and together they might find a way to overcome the difficulties, both the ones related to race and those related to the prison environment.
There was a story about a big white cock that was part of a fair in a rural town. People from all around came to see this magnificent bird. It had beautiful white feathers and a very proud stance. The owner of the cock would tell stories of how it was the best in the county, and it became a sort of local legend, with children often asking to see the famous big white cock at the fair.
One story could be in a traditional family setting. The man, after a long day at work, comes home and prepares a meal for his sick wife. He gently feeds her, showing his love and care during her time of illness.