You should take your cat to be examined by a veterinarian. The black discolouration could be calculi or be a sign of a devitalised tooth. Calculi is a deposit of mineral and organic matter which accumulates on a tooth. It is chalky or cream coloured but can be stained by food. Calculi harbour bacteria and contribute to dental and gingival disease. Calculi need to be mechanically removed whilst the cat is anaesthetised. A dead or devitalised tooth usually occurs as a result of the tooth breaking. This can be caused by trauma or by chewing hard objects. This is an extremely painful condition and can lead to further infection. If this is the case, the tooth will need to be extracted. In either case, your cat needs to go to the vet. Dental disease is extremely common in household cats, and often goes unnoticed or is ignored. Gum and tooth disease can be extremely painful. If you think about how you yourself feel when you have a tooth ache, you can have an idea of the pain and discomfort these animals feel every day. Often owners notice a massive improvement in temperament and activity once treatment has taken place. I would urge you to think about the welfare of your cat and seek veterinary attention.