Tear two large pieces of aluminum foil, lay one on top of the other and fold the sides up into a basin. Place the cubed beets into the basin and drizzle with olive oil. Stir gently to evenly coat all of the beets. Season with the salt and pepper. Tear off another piece of foil and cover the beets. Crimp the foil together to create a tight seal.
Prepare your grill for indirect heat. If you are using charcoal. place the coals to one side. If you are using propane, turn one burner to high and the other to low. If you are cooking on a pellet grill, set the temperature to High. Your target grill temperature should be around 400 to 425 degrees F.
Place the foil pouch with the beets on the grill grates over indirect heat. Cook, occasionally flipping the pouch with a spatula, for 25-30 minutes or until the beets are fork tender and slightly browned.
Serve warm or chill. Cooked beets will last several days in an airtight container in your refrigerator.