This work studies multigroup multicasting transmission in cloud radio access networks (C-RANs) with simultaneous wireless information and power transfer, where densely packed remote radio heads (RRHs) cooperatively provide information and energy services for information users (IUs) and energy users (EUs), respectively. To maximize the weighted sum rate (WSR) of information services while satisfying the energy harvesting levels at EUs, an optimization of joint beamforming design for the fronthaul and access links is formulated, which is however neither smooth nor convex and is indeed NP-hard. To tackle this difficulty, the smooth and successive convex approximations are used to transform the original problem into a sequence of convex problems, and two first-order algorithms are developed to find the initial feasible point and the nearly optimal solution, respectively. Moreover, an accelerated algorithm is designed to improve the convergence speed by exploiting both Nesterov and heavy-ball momentums. Numerical results demonstrate that the proposed first-order algorithms achieve almost the same WSR as that of traditional second-order approaches yet with much lower computational complexity, and the proposed scheme outperforms state-of-the-art competing schemes in terms of WSR.