This paper studies cooperative adaptive cruise control (CACC) for vehicle platoons with consideration of the unknown nonlinear vehicle dynamics that are normally ignored in the literature. A unified data-driven CACC design is proposed for platoons of pure automated vehicles (AVs) or of mixed AVs and human-driven vehicles (HVs). The CACC leverages online-collected sufficient data samples of vehicle accelerations, spacing and relative velocities. The data-driven control design is formulated as a semidefinite program (SDP) that can be solved efficiently using off-the-shelf solvers. The efficacy and advantage of the proposed CACC are demonstrated through a comparison with the classic adaptive cruise control (ACC) method on a platoon of pure AVs and a mixed platoon under a representative aggressive driving profile.