Many of the machine learning tasks rely on centralized learning (CL), which requires the transmission of local datasets from the clients to a parameter server (PS) entailing huge communication overhead. To overcome this, federated learning (FL) has been suggested as a promising tool, wherein the clients send only the model updates to the PS instead of the whole dataset. However, FL demands powerful computational resources from the clients. In practice, not all the clients have sufficient computational resources to participate in training. To address this common scenario, we propose a more efficient approach called hybrid federated and centralized learning (HFCL), wherein only the clients with sufficient resources employ FL, while the remaining ones send their datasets to the PS, which computes the model on behalf of them. Then, the model parameters are aggregated at the PS. To improve the efficiency of dataset transmission, we propose two different techniques: i) increased computation-per-client and ii) sequential data transmission. Notably, the HFCL frameworks outperform FL with up to 20\% improvement in the learning accuracy when only half of the clients perform FL while having 50\% less communication overhead than CL since all the clients collaborate on the learning process with their datasets.