The rapid advancement and integration of smart grid technologies have revolutionized energy systems by enabling real-time monitoring, enhanced efficiency, decentralized energy generation, and renewable energy integration. However, this increased digitization and connectivity have simultaneously exposed critical infrastructures to a growing array of sophisticated cyber threats. As smart grids evolve into complex, data-driven ecosystems, ensuring their cybersecurity becomes paramount to achieving sustainable and resilient energy systems. This paper explores the intersection of cybersecurity and smart grid sustainability, identifying vulnerabilities in advanced metering infrastructure (AMI), supervisory control and data acquisition (SCADA) systems, distributed energy resources (DERs), and communication protocols. It discusses real-world incidents and simulated attack scenarios to highlight the potential consequences of cyber intrusions on grid stability, data integrity, and energy availability. A comprehensive framework for smart grid security is proposed, focusing on proactive risk management, threat detection through artificial intelligence (AI) and machine learning (ML), blockchain-enabled data validation, and zero-trust architecture models. The framework emphasizes the importance of stakeholder collaboration, regulatory compliance, and continuous system auditing to reinforce cybersecurity postures. Additionally, this study investigates the role of digital twins in simulating cyber-physical interactions and enabling predictive threat modeling for proactive resilience. Furthermore, the paper examines policy gaps, standardization issues, and workforce capacity constraints that hinder effective implementation of cybersecurity measures across diverse energy infrastructures. Strategies for integrating cybersecurity into the lifecycle of smart grid components from design to deployment are also discussed. By aligning technological innovation with robust cybersecurity governance, the paper aims to support the development of secure, adaptive, and sustainable smart energy systems capable of withstanding emerging cyber threats. The insights provided are intended to guide policymakers, grid operators, technology developers, and researchers in fortifying energy systems against cyber vulnerabilities while ensuring the continued advancement of clean and intelligent energy solutions. Ultimately, safeguarding smart grids is not merely a technical imperative but a foundational element for achieving long-term energy sustainability and national security in the digital era.