This is what I suspected the OP meant--if you use YouTube for a while, the total data downloaded (which is what the Data Usage screen tells you) will build up. It just tells you how much data has been downloaded from the web over a period of time, not how much storage has been used. The downloaded data does NOT build up indefinitely in your storage.
As I mentioned before, YouTube will store some data in its cache, but it shouldn't reach the 6 GB range. The amount that was on your previous screenshot is more like it, in the MB range.
Sent from my DROID RAZR using Android Central Forums