Ground deformation is regarded in volcanology as a key precursor signal preceding volcanic eruptions. Satellite-based Interferometric Synthetic Aperture Radar (InSAR) enables consistent, global-scale deformation tracking; however, deep learning methods remain largely unexplored in this domain, mainly due to the lack of a curated machine learning dataset. In this work, we build on the existing Hephaestus dataset, and introduce Hephaestus Minicubes, a global collection of 38 spatiotemporal datacubes offering high resolution, multi-source and multi-temporal information, covering 44 of the world's most active volcanoes over a 7-year period. Each spatiotemporal datacube integrates InSAR products, topographic data, as well as atmospheric variables which are known to introduce signal delays that can mimic ground deformation in InSAR imagery. Furthermore, we provide expert annotations detailing the type, intensity and spatial extent of deformation events, along with rich text descriptions of the observed scenes. Finally, we present a comprehensive benchmark, demonstrating Hephaestus Minicubes' ability to support volcanic unrest monitoring as a multi-modal, multi-temporal classification and semantic segmentation task, establishing strong baselines with state-of-the-art architectures. This work aims to advance machine learning research in volcanic monitoring, contributing to the growing integration of data-driven methods within Earth science applications.