I've already answered this in my answer to Do roads really cost gold to maintain?. I really believe we can't answer that question without answering this one, making this one a duplicate, but as long as this one is open, I'll help.
Roads you build in Neutral Territory cost just as much as road in Your Territory.
How much that is seems to vary by difficulty, see Do roads really cost gold to maintain? for the full chart.
Roads in Another Nation's Territory cost YOU nothing.
This is the working theory, in need of further testing when I get the chance. Again, see the other question for faster updates, although I will come back here and edit once we have full information.
Finally, as mpenrow already said, you can get the effects of luxury resources throughout your empire without trade routes, so that is not a concern. And remember the hex with the luxury resource itself does NOT need a road. Roads are really only for moving units and connecting cities for trade in Civilization 5.