Is America a culture of cultures?

It is unclear what the question is asking about. "Culture of cultures" is not a commonly understood term.

If the question is asking whether the US is a place dominated by multiculturalism, the answer is: No. The United States is a melting pot as opposed to a salad bowl. Each person who comes to the United States is expected to become an American and adopt American values and social protocols. Unlike salad bowl cultures, like Canada, a person is not encouraged to truly be diverse.