I am sure there is some error in your observation, or you have not described your your observation correctly, with all the accompanying conditions when you observed ice cubes sinking.
Irrespective of their size ice cubes will always float. It is possible that with too many ice cubes in a glass some will be pushed below the surface of the ice, because weight of the ice above them is pressing them down. But the ice cubes will never sink to the bottom of the glass without anything pressing them down.
In this case, Archimede's law gets into action. The biggest cube has dislocated a larger volume of water that pushes up the cube to the water surface.