The Accelerated HPC in the Cloud-Edge Continuum (AHPC³) workshop is a leading forum for presenting the latest advances in the convergence of high-performance computing (HPC) with cloud-edge continuum architectures. AHPC³ focuses on innovative solutions for sustainable, energy-efficient, and intelligent execution of data-intensive and AI-driven workloads across heterogeneous infrastructures, promoting dynamic orchestration, network-aware optimizations, and federated learning across distributed environments.