Cooperative driving with V2V communication is under extensive investigation, because of its potential to increase the safety, reliability, connectivity, and autonomy of transportation systems. This paper studies the problem of connected cruise control (CCC) for a platoon of human-driven and autonomous vehicles. Motional data, such as distance and velocity information, are transmitted by vehicle-to-vehicle (V2V) communication between connected vehicles. Taking into account the communication latency and unpredictable behavior in the leading vehicle, we formulate the CCC problem as an adaptive optimal control problem with input delay and disturbance. A novel data-driven control solution is proposed for the vehicle platoon, which guarantees that each vehicle can achieve safe distance and desired common velocity. Incorporating adaptive dynamic programming technique with sampled-data system theory, a data-driven adaptive optimal controller is learned from sampled data, without the knowledge of the human or vehicle dynamics of the platooning vehicles. Stability and robustness analyses are provided by means of input-to-state stability theory. Numerical results confirm the efficacy of our method.