Answer
Ice cubes float lower in a mixed drink than in water. The buoyant force on an object equals the weight of the displaced fluid. In the less dense mixed drink, the cubes must be lower to displace enough liquid to equal their weight.
An object sinks when it is denser than the fluid, which explains why ice cubes are submerged in a cocktail. A cocktail contains a large amount of alcohol, which is less dense than both water and ice.