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.
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Check internal temperature of ham after first removal; if ham has started to brown, glaze once, cover with foil, and glaze only once more. The glaze will induce the browning.
The nutrition data for this recipe includes the full amount of the glaze ingredients. The actual amount of the glaze consumed will vary.