Yes there is a connection between drinking and cancer especially for heavy drinkers. In fact the World Health Organization classifies alcohol as a carcinogen! A recent study of 135,000 health professionals supported this claim. It was reported that within 30 years heavy alcohol consumption increased the risk of esophageal, oral, liver, colorectal and breast cancers.
Light to moderate drinking was associated with a minimally increased risk of cancer overall. Once again moderation is the word.