Structural stability is a necessary condition for successful construction of an assembly. However, designing a stable assembly requires a non-trivial effort since a slight variation in the design could significantly affect the structural stability. To address the challenge, this paper studies the stability of assembly structures, in particular, block stacking assembly. The paper proposes a new optimization formulation, which optimizes over force balancing equations, for inferring the structural stability of 3D block stacking structures. The proposed stability analysis is verified on hand-crafted Lego examples. The experiment results demonstrate that the proposed method can correctly predict whether the structure is stable. In addition, it outperforms the existing methods since it can accurately locate the weakest parts in the design, and more importantly, solve any given assembly structures. To further validate the proposed method, we provide \textit{StableLego}: a comprehensive dataset including 50k+ 3D objects with their Lego layouts. We test the proposed stability analysis and include the stability inference for each corresponding object in StableLego. Our code and the dataset are available at https://github.com/intelligent-control-lab/StableLego.