Cloud-powered solutions have emerged as transformative forces in healthcare data analytics, revolutionizing how healthcare organizations process, analyze, and utilize patient data. These solutions leverage data science, Large Language Models (LLMs), and machine learning technologies to revolutionize patient care and enhance healthcare system efficiency. This comprehensive study analyzes the Cloud infrastructure integration in healthcare facilities demonstrating a remarkable 72.3% improvement in clinical documentation efficiency and average annual savings of $4.7 million per facility. Also, these technologies enhance healthcare accessibility, improve public health monitoring, economic outcomes, and strengthen data security on healthcare delivery across urban and rural settings. This article explores the impact of cloud computing across five critical dimensions: infrastructure capabilities, data science, machine learning integration, LLM applications, and societal impact. This paper provides quantitative evidence of cloud computing's role in advancing global healthcare innovation on precision medicine, real-time insights, unparalleled operational efficiencies while ensuring robust security and regulatory compliance.