For structures with highly heterogeneous material distributions, capturing fine structural details often demands extremely high-resolution numerical discretization. Due to the need to solve large-scale linear systems, conventional finite element methods incur substantial computational costs when applied to such problems. While substructure-based model reduction techniques can alleviate the computational burden on coarse grids, the required reduction (condensation) process is time-consuming. Existing machine learning-enhanced methods provide a promising alternative by replacing the online condensation with a learned surrogate. However, errors introduced by machine learning may yield non-physical results, and learning becomes more challenging as the substructure dimension increases. In this work, we leverage the symmetry of cubic substructures to propose a simplified learning strategy, which requires learning only the fundamental part of the shape functions. Furthermore, we enforce the rigid-body properties of the shape functions through a projection-based correction, significantly enhancing the neural network’s prediction accuracy and physical consistency. The proposed method achieves twice the accuracy of existing approaches in both prediction and analysis accuracy. Numerical examples show that the method maintains performance and consistency in classical benchmark problems. Moreover, it exhibits improved stability in optimizing lattice structures, which are highly sensitive to mechanical responses.