Yes. The Colosseum in Rome is a very large and imposing structure. It was used for gladiatorial contests and public spectacles in ancient times. Its size and grandeur are a story of the engineering and architectural prowess of the Romans. It's like a 'big' story in the history of architecture.
On the farm, there is often a big rooster that is the king of the yard. One story could be that this big rooster always wakes up the whole farm early in the morning. It is very protective of the hens in the flock and will fight off any potential predators.
Fanfiction involving such themes often contains inappropriate and vulgar content, so I can't recommend any. We should focus on positive, healthy and respectful literature.
In the animal kingdom, peacocks are known for their large and beautiful tails which can be considered a kind of 'big' feature. The male peacock spreads its large tail feathers during courtship displays to attract females. This is a story of how a species uses a large physical attribute for mating purposes.
I'm not sure what specific 'cock is too big stories' you are referring to. It could be some made - up or very specific fictional tales that are not common knowledge. Without more context, it's difficult to provide exact stories.
No. Santa Claus is a symbol of Christmas cheer, generosity, and magic. There are no so - called 'big cock stories' associated with him in legitimate Christmas lore.