Networks are widely used to model objects with interactions and have enabled various downstream applications. However, in the real world, network mining is often done on particular query sets of objects, which does not require the construction and computation of networks including all objects in the datasets. In this work, for the first time, we propose to address the problem of query-specific network construction, to break the efficiency bottlenecks of existing network mining algorithms and facilitate various downstream tasks. To deal with real-world massive networks with complex attributes, we propose to leverage the well-developed data cube technology to organize network objects w.r.t. their essential attributes. An efficient reinforcement learning algorithm is then developed to automatically explore the data cube structures and construct the optimal query-specific networks. With extensive experiments of two classic network mining tasks on different real-world large datasets, we show that our proposed cube2net pipeline is general, and much more effective and efficient in query-specific network construction, compared with other methods without the leverage of data cube or reinforcement learning.