Whether ice cube melts faster in water or in the air may depends on many factors such as the ratio/amount of water to ice, the temperature of the water, the temperature of the atomsphere, the container you use to put the water in, the surface you put the water to melt (is it on a wooden table, granite table?).
I just did this experiment using two ice cubes about the same size. I put the cubes in plastic bowls. In one bowl, I pour room temperature water just enough to cover the ice cube and in the other bowl, I just put in the ice cube. When the ice cube in water completely melted, the water without the water only melted about 10-15%.
If you watch ice cubes melt, it may be hard to tell whether they melt faster in water or air, but if the water and air are the same temperature, ice melts more quickly in one than in the other. water, assuming the air and water are the same temperature. Longer answer: Usually water, because the molecules in liquid water are more tightly packed than the molecules in air, allowing more contact with the ice and a greater rate of heat transfer. Also, water has a higher heat capacity than air.