What's the cause of presence of black or yellow and sometime even white color of the tooth with dental caries?

Is black, it's worse: Dental caries do not cause the tooth to become black. That usually means the dental root or nerve has been destroyed. Get ye to the dentist - now. If it is white, off-white, very light yellow--sounds normal, unless the surrounding teeth are a different shade.

Staining: The color of the decay varies depending on the amount of the decay present and where on the tooth the decay is located..The extent of the decay through the enamel will cause different transparencies and thus different colors.

Decalcified enamel : When a tooth decays the enamel looses calcium and decalcifies and changes color

Decay: Caries or decay can be almost any color. When Bactria decalcify the enamel of a tooth and start "eating" the organic materials of the tooth, the by product is an inorganic material that can be most any color.

Dental caries: The process of decaying from within the tooth is causing these discolorations

Spots?: Are these spots or patches, the white color could be due to hypocalcification or low mineral content of the tooth and the causes vary from genetics to sickness in childhood to low or excessive fluoride in the drinking water. The yellow color could be due to plaque or stains and black could be due to dental caries or stains.