Rabbits have a very specialized (some would say sensitive) digestive system. Feeding too much cabbage to rabbits is likely to give them gas and diarrhea. This is because the bacteria in the rabbits digestive tract ferment everything that the rabbit doesn't digest. Under normal conditions the hay that the rabbit eats takes time to ferment and it slowly supplies bacteria with the nutrients they need to grow. These bacteria then produce B-vitamins and other nutrients for the rabbit. This can go bad when rabbits eat things like cabbage that are easily fermented by bacteria. This causes bad bacteria to out grow the good bacteria and produce the gas that causes bloating. If the situation gets worse then your bunny may end up getting diarrhea and loose its appetite. A loss of appetite often leads to death so it is very important to make sure your bunny keeps eating. For this reason rabbits are healthier when fed well balanced pellets that are low in carbohydrates (sugar and starch) but high in fiber and specific nutrients.
Adult rabbits will do best when fed pellets that are soy and grain-free, rich in timothy hay, and supplemented with specific vitamins, minerals, and even whole oil seeds like flax. This type of diet will promote optimal health and a beautiful fur coat. It will also make a positive impact on the playfulness of your pet rabbit.
Baby rabbits require a high-energy diet rich in fiber and high in fat "like mamma's milk." This will promote healthy growth and prevent digestive troubles that are common to baby rabbits fed other brands of food.
So can rabbits eat cabbage? If you do feed them cabbage test it out in very small amounts and be careful not to feed too much... only as a treat!