Abstract: The analysis of spatiotemporal event data is essential for informed decision-making in domains such as disaster response, conflict analysis, or intelligence investigations. However, the complexity and interdependence of spatial, temporal, and multiple thematic attributes pose significant challenges for both analysis and visualization. While space-time cubes (STCs) present a powerful integrated visualization technique to analyze this kind of data, existing approaches often lack support for complex exploratory workflows, thus limiting the ability to derive meaningful insights. We address this gap by introducing STcubeOperator, a novel framework that models analysis tasks through space-time cube operations, considering them in context of visualizations, interactions, and computational choices, and implement them in an interactive visual analytics environment. By expressing analysis tasks as a sequence of multiple elementary operations--such as filtering, chopping, and flattening--our approach enables analysts to dynamically explore data from different perspectives. We further provide an open-source prototype implementing the operations in a 3D interactive environment to facilitate task-based exploratory analysis of spatiotemporal event data. We demonstrate the applicability of our framework with a case study based on real-world data on strategic and military operations in the Russia-Ukrainian War, showing its capabilities to reveal spatiotemporal patterns. An expert user study (n=8) shows how specific tasks can be solved with our framework, highlights the versatility of our approach, and provides valuable insights on which operations experienced analysts utilize in practice.