Consider it doesn't collide with any other objects. Would it be preserved perfectly in the vacuum or would its surface be damaged by anything like UV rays, radiation, gas, space dust, etc?
There are three main space weathering processes that will affect the surface of the marble.
Cosmic rays, high energy particle from the sun and beyond, will hit the surface. This can change the chemistry of the surface.
Solar wind particles, hydrogen and helium, can become implanted in the surface
Micrometeoroids will impact the surface, causing small craters, melting, and the inclusion of other elements such as iron.
These processes will tend to change the surface, developing a patina on a timescale of a hundred thousand years. The surface will darken (though as marble is not a typical rock in asteroids, there isn't any direct evidence of what happens with marble.
Marble is largely CaCO3, and this is in a equilibrium with CaO and CO2. At standard temperatures and even the very low partial pressure of CO2 in the atmosphere, this equilibium favours CaCO3. In our atmosphere one needs a temperature of 550⁰C to decompose Calcite. However in space there is no CO2, and so the Calcite would very slowly decompose to CaO. Calcium in meteorites is mostly in the form of CaO.
Cosmic rays may impinge pressure on the statue, which will deteriorate its surface. Various electromagnetic rays (X-ray, Gamma rays and Infrared) can interact with the chemical elements of the statue.
Piggy backing on James K's answer above, there is a fourth process depending on the proximity to any star, which is thermal stress.
As the statue rotates with respect to any "near" star, thermal stress will lead to surface weathering over time: https://en.wikipedia.org/wiki/Weathering#Thermal_stress
Thermal stress weathering (sometimes called insolation weathering) results from the expansion and contraction of rock, caused by temperature changes. For example, heating of rocks by sunlight or fires can cause expansion of their constituent minerals. As some minerals expand more than others, temperature changes set up differential stresses that eventually cause the rock to crack apart. Because the outer surface of a rock is often warmer or colder than the more protected inner portions, some rocks may weather by exfoliation – the peeling away of outer layers. This process may be sharply accelerated if ice forms in the surface cracks. When water freezes, it expands with a force of about 1465 Mg/m^2, disintegrating huge rock masses and dislodging mineral grains from smaller fragments.