This problem is referred to as "hollow cubes" and it does cause the cubes in the ice bucket to stick together.
If the refrigerator and the icemaker are level hollow cubes are caused by 1 of 2 things.
The water fills into the end of the icemaker opposite the motor and controls. If the water doesn't fill all of the ice molds the one closest to the motor will have a partial fill. The thermostat senses the temperature of this mold and when the thermostat closes the harvest cycle begins. A partial fill causes this mold to cool faster than the other molds so the icemaker harvests partially frozen cubes from the other molds.
To check this put your finger into the molds and see if the front one is less full than the others. I am sending you an image showing how to adjust the water level of the icemaker. If the water level changes again after you have adjusted it, replace the refrigerator water valve.
The second thing that can cause hollow cubes is a defective thermostat inside the icemaker. If this thermostat fails it is slightly more expensive and much less work to replace the entire icemaker. If the water level in the ice molds is all the same I would replace the icemaker.