I have to write a paper concerning culture (he made the topic very broad on purpose) and I want to discuss how gun powder was used differently in different parts of the world. But is it fair to call gun powder a part of culture? It was technically used as entertainment in China, and artillery elsewhere.... Is artillery use a part of culture?
You can write your paper about that.
People have written cultural histories about firearms. For instance, Giacomo Macola wrote a chapter in A Cultural History of Firearms in the age of Empires about how Ngoni military culture resisted adoption of firearms, because machismo and soldierly virtue encouraged facing the enemy in hand-to-hand combat rather than at a distance.
Other chapters of the same book cover the role of firearms in 19th century big game hunting; as well as the legal fights African-Americans put up between 1865-1940 to secure the right to own firearms, for protection against race-based violence.
You can certainly broaden the scope to examine how culture informs the many uses of gunpowder. For instance, in addition to fireworks and military uses, you can explore how societies with strong traditions of mining chose to adopt or reject the use of gunpowder for mining. Or how firearms were included (or not) in hunting.
Other questions you could ask are "what were the social rules around gunpowder use". That is to say: was working with gunpowder something women could do, or only men? Could every class of person use it, or was it restricted to specialists? Did people who manufactured gunpowder (or firearms, or fireworks, or artillery) try to restrict that knowledge, or did they allow that knowledge to flow freely? Did the Pope, or priests, or ulama or buddhist abbots say anything praising or condemning firearms or explosives or fireworks?
It was technically used as entertainment in China, and artillery elsewhere...
Careful there. Chinese people developed gunpowder into fireworks as well as weaponry like fire-lances, fire-carts, and even cannons.
If you had planned to write a paper about how it says something about culture that the Chinese invented gunpowder and used it for peaceful purposes, while Islamic and European cultures adopted the technology and turned it to military purposes....well, that is not an accurate framing. The Chinese were quick to use gunpowder for military purposes, and they did experiment in using cast iron for cannon making.