A dual-filled gum piece is provided having a first cavity filled with a liquid filling and a second cavity filled with a powder filling. The gum pieces are produced by extruding a gum rope having two separate channels respectively filled with liquid and powder, sizing and shaping the gum rope, cooling the gum rope, cutting the rope into discrete gum pieces, and finally cooling the gum pieces. The gum pieces optionally can be coated with a hard coating. In other aspects for single- and dual-filled gums, a process for making the gum pieces employs a rope sizer that reduces the diameter of the gum rope and shapes it to have a non-round cross-section, and a multi-story cooling tunnel having individually motor-driven conveyors.