Tangible interactions have been widely studied, involving various objects equipped with different sensors in different application domains. Among these, tangible cube interfaces represent a particularly promising modality for these domains, including educational contexts of use, as they promise to improve learning. However, gestural interaction with tangible cubic objects remains mostly task- or domain-specific, limiting their reusability and generalizability. This paper investigates gestural interaction with tangible cubic objects, focusing on AudioCubes, through a mixed-method approach that integrates a systematic literature review, gesture elicitation studies, and usability evaluations. The findings of this study will contribute to the following: (i) a classification of reusable gestures for tangible cubes, (ii) some insights into common barriers for diverse user groups, including children and users with motor or cognitive differences, and (iii) some design implications for more adaptable and generalizable gestural interaction with tangible cubes.