If I understand the object of the question correctly "packed brown sugar" refers to brown sugar that will pack into a semi-solid mass instead of remaining loose, i.e., it's the moist kind that is common in the US (and perhaps other places).
Those who suggest German Rohrzucker or Rohzucker, etc., don't understand what it being asked, as these products are not the same as US brown sugar in that they do not pack and their taste is much milder. Also, as is the case with most German sugars, their crystal size is much larger, which can negatively affect the results of recipes designed for the finer US crystal size.
The best substitute is what snickerdoodle recommended, as this is all that brown sugar in the US is: adding molasses to white sugar (or, just adding the two separately to the recipe rather than trying to mix them together separately).
Of course, molasses isn't the easiest product to find in Germany (perhaps in "Reformhäuser"...? I know I've seen it somewhere.)But, Cynthia Barcomi (from the US, operates a great bakery/cafe in Berlin, cookbook author) suggests using sugar beet syrup ("Zuckerrübensirup"), such as from Grafschafter, instead of molasses. It's more readily available, and is a pretty good substitute. The taste is slightly different, but similar.