As per your description the spots can be associated with either strain or cavity. It can be differentiated only on a clinical check up by a dentist. As the grinding surfaces of back tooth are irregular they tend to retain food particles n stains. If they are properly brushed and cleaned cavities or stains are not formed. Once they formed they need to be treated either with sealants or filings.....

Dear sir/Madam, black discolouration of the teeth can be due to a number of reasons, the most common being dental Caries or Tooth decay. Another probability can be some sort of stains. However this situation requires a dentists intervention and I highly recommend you to visit the dentist.