No, it is not possible for a planet to be completely formed out of liquid water, including the inner core. The formation and composition of planets are determined by a combination of factors such as distance from the star, temperature, and the materials available during the planet's formation.
Water is composed of hydrogen and oxygen, and it exists in a liquid state within a specific range of temperatures and pressures. In the conditions found in most planetary interiors, the temperatures and pressures are far beyond the point at which water would remain in a liquid state.
In the case of Earth, for example, the inner core is solid due to the intense pressure it experiences, while the outer core is molten iron and nickel. This is because the pressure and temperature in the Earth's core are much higher than the conditions required for water to exist as a liquid. Similarly, other rocky planets in our solar system and beyond have solid cores and may or may not have liquid water on their surfaces depending on various factors.
While water can exist on the surface of a planet in the form of oceans, lakes, or ice, the internal composition of a planet is typically determined by the materials available during its formation and the processes that occur over time.