This paper presents a novel approach for cyber-attack detection and mitigation in DC microgrids. The proposed method combines the Cubature Kalman Filter (CKF) with a Nonlinear Unknown Input Observer (NUIO) to simultaneously estimate system states and identify malicious intrusion signals. First, the dynamic model of the microgrid, incorporating uncertainties caused by cyber-attacks, is formulated. Then, the CKF enhances the accuracy of state estimation, while the nonlinear observer is designed to reconstruct malicious signals injected by attackers. To evaluate the effectiveness of the proposed method, simulations are conducted on a DC microgrid under common cyber-attacks, including data injection and false signal attacks. The results demonstrate that the proposed approach detects cyber-attacks with an accuracy of 93.2%, whereas the Extended Kalman Filter (EKF) achieves only 84.5%. Moreover, attack reconstruction errors are reduced by 27%, leading to a 14% improvement in the system's dynamic stability. These findings confirm that integrating the Cubature Kalman Filter with a Nonlinear Observer provides a robust and efficient solution for enhancing DC microgrid resilience against cyber threats. This framework can serve as a generalized approach to improving cybersecurity in modern power networks and energy distribution systems.