At the moment the MassProperties only exposes the Moment of Inertia around the component's Centre of Gravity:
MassProperties.XYZMomentsOfInertia
Though the Global values (which are available in the UI) can be calculated, it would be nice to make them available in the API too, e.g.
MassProperties.GlobalXYZMomentsOfInertia
See discussion on forum: http://forums.autodesk.com/t5/inventor-customization/ivextget-moments-of-inertia/m-p/4860438