There is no train from Cancun to Belize. At one time, the 1970s and into the 80s, there was train service from Mexico City to Merida in the Yucatan, and also on the WEST side of the Yucatan to Campeche and down to Cuidad Hildago connecting in Guatemala, but I don't think that in modern times there has been service to Chetumal and Belize. The last train in Belize, a banana train, was probably 60 years ago.
Mexican buses are nice, though. Lot nicer than U.S. airlines.
Belize First Magazine http://www.turq.com/belizefirst/