Trim excess fat from ham, leaving 1/4-inch layer of fat. Score fat in a diamond pattern using a sharp knife. Place ham on a rack in a large roasting pan and pour cola in pan, reserving about 1/4 cup for the glaze. Season ham with allspice and salt.
Bake in preheated oven, basting every 15 minutes with pan juices, for 1 hour.
Combine strawberry jam, brown sugar, and apple brandy in a saucepan over low heat; cook and stir until sugar is dissolved, about 5 minutes. Remove pan from heat and stir reserved cherry cola into the glaze; brush onto ham to coat.
Return ham to oven to continue cooking, brushing with the glaze 2 to 3 times more as it cooks, until an instant-read thermometer inserted into the center reads 140 degrees F (60 degrees C), 30 to 45 minutes more. Tent ham loosely with aluminum foil and set aside for 30 minutes before carving.