DIAGNOSIS This is "clumping" or "bridging," caused by the ice sitting in the warm, humid air of the basket for too long between cycles. The surface of the cubes partially melts and then re-freezes together.
FIX You need to reduce the ice's dwell time in the basket. Set the machine to the "Small Cube" setting if you're using the "Large Cube" setting—smaller cubes have less surface area to melt and stick. More importantly, empty the ice basket into your freezer's storage bin more frequently. Don't let it fill to the "Full" sensor.
IF THAT DIDN'T WORK High kitchen humidity is the culprit. Move the ice maker to a less humid location (not right next to the sink, dishwasher, or stove). Running a dehumidifier in the room will also dramatically reduce clumping.
HEADS UP Never store the ice long-term in the machine's basket. These are production baskets, not storage bins. For dry, separate cubes, always transfer fresh ice to a sealed container in your freezer.