The color of the dentin of a tooth when it is undergoing the process of tooth decay is the color of the dentin normally. The degenerative aspect of the carious process itself does not confer a color. So yes, a cavity
can be white. The color of brown and black is part of the healing process. So when fresh dentin breaks down, it is white, and when it is rebuilt in a visible way, it usually darkens.
However, this usually is within a cavernous hole of a tooth into which you probably will not be able to see.