Correct, the V6 and V8 engines are built in Győr, Hungary, at a very large Audi-operated plant. It is a very modern factory, the first part of it was opened in the mid 1990s but in the last few years it has expanded quite a bit. I have visited it, but they do not offer public tours. They also make the Audi TT at this same factory - but their main activity is making engines.
A poster from the engine factory in Gyõr