|If I were to heat up a brownie and a white piece of cake, would the brownie heat up faster by radiation transfer because of its darker color? — B
In principle, the brownie would heat up faster by radiation in a hot environment and cool off faster by radiation in a cold environment. A black object is better at both absorbing thermal radiation and emitting thermal radiation, so the brownie would soak up more thermal radiation in the hot environment and give off more thermal radiation in the cold environment.
In practice, however, most of the radiation involved in baking these desserts and letting them cool on a kitchen counter is in the infrared and it's hard to tell just what color a brownie or cake is in the infrared. It's likely that both are pretty dark when viewed in infrared light. Basically, even things that look white to your eye are often gray or black in the infrared. Thus I suspect that both the brownie and cake absorb most of the thermal radiation they receive while being baked and emit thermal radiation efficienty while they're cooling on the counter.