<p>This paper addresses the sampled-data boundary stabilization problem of a cascaded system comprising an ordinary differential equation (ODE) and two coupled reaction-diffusion partial differential equations (PDEs), and in particular, tackles challenges arising from the spatial interconnections among PDE states and arbitrarily large but bounded distributed delays in the input channel. Initially, a continuous-time control law is developed using a backstepping-forwarding transformation, with the global exponential stability of the closed-loop system established. Subsequently, a sampleddata control strategy is obtained by applying a sample-and-hold mechanism to the continuous-time signal. The stability analysis for this digital implementation integrates spectral analysis of the discretized target system with input-to-state stability (ISS) estimates for the infinite-dimensional dynamics. It is demonstrated that global exponential stability is preserved, provided that the sampling period meets a specified spectral radius condition. Numerical simulations confirm the effectiveness of the proposed control strategies and validate the stability bound on the sampling period.</p>