The rotational normal modes of the planet Mars are computed using a numerical approach. We deduce the associated resonances in the nutations induced by the external gravitational forcing from the Sun, Phobos, and Deimos. In particular, the influence of a possible solid inner core inside a liquid core is investigated. A normal mode associated with the inner core (Free Inner Core Nutation (FICN)) is computed, as well as the associated resonance effects in the nutations. For a small inner core, before the eutectic composition of the outer core is reached, the FICN effect on nutation is negligible. For a large inner core it can be very important, and for some nutations it can greatly decrease the resonance effect of the classical Free Core Nutation. Future observations of Mars nutation resonances will therefore provide information about the inner core.