Hip Hop has permeated the problems in the world.
Not really. It would help to have some context about what you are discussing here. But, we really don’t use “permeated” for things that cause or have problems. A good alternative verb is underlies, or contributes to.
In addition, “the problems in the world” sounds very awkward. You might change it to “some problems of the world” or “many global problems” to make it sound better.
- Hip hop underlies a variety of global problems.
- Hip hop contributes to many of the problems around the world.