Creativity plays an important role in many learning activities but how to enhance creativity with the support of modern computer tools deserves further studies. In this paper, we propose a game-based collaborative creativity support system called Idea Storming Cube to support creative thinking and help a user form a perspective-shift thinking habit. The system analyzes the knowledge acquired from the history of user inputs and compares it with the ideas possessed by the domain expert and other users in the current brainstorming group. The system is designed to provide user-, goal-and context-sensitive supports with this mechanism that stimulates more divergent thinking. We have implemented the proposed game with a magic-cube-like HCI for collaborative idea generation. A case study for preliminary evaluation of the system is also reported in this paper.