This paper explores the cubic-regularized Newton method within a federated learning framework while addressing two major concerns: privacy leakage and communication bottlenecks. We propose the Differentially Private Federated Cubic Regularized Newton (DP-FCRN) algorithm, which leverages second-order techniques to achieve lower iteration complexity than first-order methods. We incorporate noise perturbation during local computations to ensure privacy. Furthermore, we employ sparsification in uplink transmission, which not only reduces the communication costs but also amplifies the privacy guarantee. Specifically, this approach reduces the necessary noise intensity without compromising privacy protection. We analyze the convergence properties of our algorithm and establish the privacy guarantee. Finally, we validate the effectiveness of the proposed algorithm through experiments on a benchmark dataset.