Well, I have to admit I don't have much knowledge/source on the economical situation and statistics of the colonies and similar territories of the non-german powers at that time but for the german colonies I've looked up some source :
In 1913/1914 following colonies/"Schuttzgebiete" had a negative balance sheet for the empire
Namibia, German South-West
Tanzania, German East Africa
New-Guinea, Kaiser-Wilhelm Land
Means : these received more money from Berlin, than Berlin received from them. though their absolute amount was esp. for the last two rather negligable.
Most of these 'cost' for Berlin came from investment goods :
and the costs for their installation
as there were mayor development operations going on esp. in Kiautschou (development of the naval base there), Kamerun and East Africa (mayor infrastructure development => railways).
Interestingly these mayor regions of ongoing development were the colonies with a negative trade-balance as well :
Kiautschou, East Africa and Kamerun
while all other colonies had a positive trade balance after 2-3 decades of german administration. The trade 'neagtives' of the other colonies were also 'dwindling' over the last 5-10 years before the Great War and would most likely be even smaller if the 'public' investments of the state might be de-accounted for.
So, alltogether ... the german colonies were well on their way to become a considerable plus in economics as well (and possibly even more important) a plus in global political weight
Source for 'short' :
Somewhat more 'time-consuming :
(the statistical alamnacs of the German Realm/ Deutschen Reiches)