We propose an extension of the well-known Space-Time Cube (STC) visualization technique in order to visualize time-varying 3D spatial data, taking advantage of the interaction capabilities of Virtual Reality (VR). The analysis of multidimensional time-varying datasets, which size grows as recording and simulating techniques advance, faces challenges on the representation and visualization of dense data, as well as on the study of temporal variations. First, we propose the Space-Time Hypercube (STH) as an abstraction for 3D temporal data, extended from the STC concept. Second, through the example of embryo development imaging dataset, we detail the construction and visualization of a STC based on a user-driven projection of the spatial and temporal information. This projection yields a 3D STC visualization, which can also encode additional numerical and categorical data. Additionally, we propose a set of tools allowing the user to filter and manipulate the 3D STC which benefits from the visualization, exploration and interaction possibilities offered by VR. Finally, we evaluated the proposed visualization method in the context of the visualization of spatio-temporal biological data. Several biology experts accompanied the application design to provide insight on how the STC visualization could be used to explore such data. We report a user study (n=12) using non-expert users performing a set of exploration and query tasks to evaluate the system.