The cubature Kalman filter (CKF), while theoretically rigorous for nonlinear estimation, often suffers performance degradation due to model-environment mismatches in practice. To address this limitation, we propose CKFNet-a hybrid architecture that synergistically integrates recurrent neural networks (RNN) with the CKF framework while preserving its cubature principles. Unlike conventional model-driven approaches, CKFNet embeds RNN modules in the prediction phase to dynamically adapt to unmodeled uncertainties, effectively reducing cumulative error propagation through temporal noise correlation learning. Crucially, the architecture maintains CKF's analytical interpretability via constrained optimization of cubature point distributions. Numerical simulation experiments have confirmed that our proposed CKFNet exhibits superior accuracy and robustness compared to conventional model-based methods and existing KalmanNet algorithms.