gabriel, it's the same here where I live, and usually, in my minimal experience with apartment-living, the owner/manager handles it promptly.
I lived in a townhouse for a while after my divorce and had a very strange set of neighbors who would fight constantly at 2am. The screaming would be so loud and so intense that it would often wake the kids. I tried talking to the neighbors, but they acted like I was invading their privacy and stepping over the line by even mentioning it to them. So I took it to the owner of the properties and he immediately issued a written warning or whatever it is legally called. I also spoke with the tenants on the other side of their unit and asked them to file a complaint if it was bothering them. It was. They did. While I'm not sure of the legalities involved, after several written warnings, the owner ended up evicting them because of all the complaints.
So filing a complaint is a good idea if you'd eventually like to get some peace and quiet. I'd also recommend talking to the other tenants to see if they are having the same issues with his noise. If so, multiple complaints by unrelated parties to the owner.manager would really bring the situation to a close quickly, IMO.
And one more thing - My boyfriend is a night-owl and a musician, and when he gets the drum machine out at night, he uses headphones! I'd think this guy could be courteous enough to do that in the evenings and at night at the least. I believe almost all the drum machines have headphone jacks for that very reason - monotonous drumming is torturous!