One thing you can do is examine the select statement issued during the cube build. if your cube has been optimized you should see
Select ColA,ColB From FactTable.
If you don't your cube is not optimized. Not using 2k for a while I am not 100% what menu it is under but if you open the cube designer and go through each of the menu drop downs you should see Optimize Cube or Optimize Schema something like that, again it has been a while. If you do this it will help, however for the optimization to work a few things have to be followed in the cube and dimension design. The 2 main points being.
1) The leaf level of your dimensions must have uniqueness of the keys set to true.
2) Your Dims and fact tables must join at the leaf level of the dimension. Yea I know this one sounds like a no brainer but very early in my OLAP career I had an instance where the Leaf od the Date dim was day, we also carried a Month Key. There was an instance where the fact table supported either a day or month join, all reporting of this data was at the month level so I joined at the month. OOPS! that was not the right decision.
Good Luck and hope this points you in the right direction.
Also if you venture in to SSAS on 2005 you may want to push the money people to spring for Enterprise as Cube partitionin is offered only in Enterprise and addresses the issue you are currently experiencing.
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