An ice making assembly includes a support and a mold rotatably mounted to the support configured for forming an ice cube therein. The mold has a base, a side wall attached to the base, and an opening in the side wall spaced from the base. An auger has a shaft with a proximal end fixed to the base of the mold, a distal end outside of the mold, and a central section between the proximal end and the distal end and extending through the opening. The auger also has a threaded portion. An inner mold is non-rotatably fixed to the support and extends into the mold. The inner mold defines an outer shape of the ice cube. The inner mold has at least one wall non-concentric with reference to a center line of the auger. A motor rotates the mold and auger relative to the support and inner mold. The inner mold is configured to prevent the ice cube from rotating with the mold and auger, the auger thereby moving the ice cube out of the mold and the inner mold via the opening.