Spatial data analysis has become ubiquitous as geographic information systems (GIS) are widely used to support scientific investigations and decision making in many fields of science, engineering, and humanities (e.g., ecology, emergency management, environmental engineering and sciences, geosciences, and social sciences). Tremendous data and computational capabilities are needed to handle and analyze massive quantities of spatial data that are collected across multiple spatiotemporal scales and used for diverse purposes. CyberGIS has emerged as a new-generation GIS based on advanced cyberinfrastructure to seamlessly integrate such capabilities into scalable geospatial analytics and modeling tools. One of the key challenges and opportunities of CyberGIS research is to build an on-demand service framework that can manage underlying cyberinfrastructure resources dynamically, in order to provide responsive support for interactive online CyberGIS analytics for which users can generate massive service requests in a short amount of time. This paper presents a cloud computing approach to implementing CyberGIS analytics using cloud computing services in the CyberGIS Gateway, a multiuser and collaborative online problem-solving environment. The primary purpose of this research is to address the question of how to achieve on-demand and scalable CyberGIS analytics that provide a stable response time to the user. We do that through integration with the Nimbus Phantom cloud platform. We then investigate how the cloud platform is able to adaptively handle fluctuating requests for analytics while providing a stable response time.