mmWave FMCW radar has attracted a huge amount of research interest for human-centered applications in recent years, such as human gesture and activity recognition. Most existing pipelines are built upon conventional discrete Fourier transform (DFT) preprocessing and deep neural network classifier hybrid methods, with a majority of previous works focusing on designing the downstream classifier to improve overall accuracy. In this work, we take a step back and look at the preprocessing module. To avoid the drawbacks of conventional DFT preprocessing, we propose a complex-weighted learnable preprocessing module, named CubeLearn, to directly extract features from raw radar signal and build an end-to-end deep neural network for mmWave FMCW radar motion recognition applications. Extensive experiments show that our CubeLearn module consistently improves the classification accuracies of different pipelines, especially, benefiting those simpler models, which are more likely to be used on edge devices due to their computational efficiency. We provide ablation studies on initialization methods and structure of the proposed module, as well as an evaluation of the running time on PC and edge devices. This work also serves as a comparison of different approaches toward data cube slicing. Through our task-agnostic design, we propose a first step toward a generic end-to-end solution for radar recognition problems.