No, non-human animals do not have cultures in the way that we understand culture. A culture is a way of life that is not determined by nature or by instinct. Instead, it is a way of life that is consciously passed on from one generation to the next. It consists of knowledge and attitudes and beliefs that define that particular culture. Animals other than human beings do not have these things.
It is possible to argue that a group of animals could have something that is like a culture. They have behaviors such as hunting in specific places that are taught by one generation to the next. However, this should not be considered to be culture. So far as we know, these behaviors are essentially not cultural. They are more of matters of instinct. They certainly do not involve attitudes or beliefs.
Only human beings, so far as we know, can have true culture. Only human beings have attitudes and beliefs about things that they choose to hold. These are very different things from the more instinctual behaviors of animals.