Heh, I've never had cream/white/whitewall tires, but my royal blue tires clean up beautifully with a soft brush and Simple Green (or whatever soap you use on the rest of your bike). On the rare occasions that I feel like it's worth it. 
Actually, they're rarely so bright as when I'm riding in the rain. The combination of the water and the abrasion of the road really cleans them up. It's hot dry weather that really covers them with tar.
Congrats on the new bike! Pretty.
Speed comes from what you put behind you. - Judi Ketteler