The core of a terrestrial planet such as Mars is generally considered to evolve, as a result of cooling of the planet, from an initially entirely liquid state, through the growth of a solid inner core, to an entirely solid state. Both theoretical evolution studies and geodesy observations indicate that at least part of the Martian core is still liquid. However, at present, there is no conclusive evidence for the existence or the absence of a solid inner core. A liquid outer core and a solid inner core can strongly affect the rotational dynamics of the planet, in particular, polar motion and nutation, through resonances with three rotational normal modes of the core. For a sequence of Martian models with a growing inner core, the normal modes and their effects on polar motion and nutation are calculated from an analytical model. In particular, the frequencies of the modes and the associated resonance strengths for polar motion and nutation are studied, and the parameters of the interior structure most important for the changes of these quantities are identified. We show that the amplification of nutation and polar motion can be extremely important for particular radii of the inner core that yield resonance frequencies close to the forcing frequencies. Future observations of polar motion and nutation of Mars therefore offer a unique way to observe the deep interior of the planet.