Alcohol is less dense than water, less even, than frozen water, so, since the ice cube is denser than the alcohol in the glass, it sinks.
Does things float in alcohol?
Dense materials sink, and less-dense materials float. Water is denser than alcohol, so the alcohol floats on top of the water.
What happens to ice in alcohol?
If you've ever poured hard liquor over ice, you've probably noticed that the ice melts unusually fast. That's because alcohol brings the freezing temperature of water down significantly.