The graph convolutional network (GCN) emerges as a promising direction to learn the inductive representation in graph data commonly used in widespread applications, such as E-commerce, social networks, and knowledge graphs. However, learning from graphs is nontrivial because of its mixed computation model involving both graph analytics and neural network computing. To this end, we decompose the GCN learning into two hierarchical paradigms: 1) graph-level and 2) node-level computing. Such a hierarchical paradigm facilitates the software and hardware accelerations for GCN learning. We propose a lightweight graph reordering methodology, incorporated with a GCN accelerator architecture that equips a customized cache design to fully utilize the graph-level data reuse. We also propose a mapping methodology aware of data reuse and task-level parallelism to handle various graphs inputs effectively. The results show that Rubik accelerator design improves energy efficiency by $26.3\times$ – $1375.2\times$ than GPU platforms across different datasets and GCN models.