As an expert in astrophysics, I can tell you that an ice cube in space would undergo a process known as sublimation. This is a phase transition where a substance goes directly from the solid to the gas phase without passing through the intermediate liquid phase. The ice cube would start to lose mass as the water molecules gain enough energy to escape the solid structure and become water vapor. This process would continue until the entire ice cube has sublimated, leaving no trace of its original form. In space, there is no atmosphere to provide pressure, and temperatures can vary greatly depending on the distance from the Sun and the presence of other heat sources. The side of the ice cube exposed to the Sun would sublimate more quickly than the shaded side, which could lead to an uneven sublimation process. Additionally, the lack of convection in space means that the heat is not distributed evenly around the ice cube, further contributing to the uneven sublimation. Over time, the ice cube would gradually decrease in size, with water vapor dispersing into the vacuum of space. This process can be quite rapid if the ice cube is close to a heat source like the Sun, or it can take a very long time if it is in the cold depths of space, far from any heat source. read more >>

A comet is a rough approximation to an ice cube. If you think of what happens to a comet at various places, that's about what would happen to your ice cube. It would sublimate. The frozen mass of water would decrease in size as the water converts from a solid to a gas (without becoming a liquid) and drifts away.read more >>