We have investigated the microwave response of a transmon qubit coupled directly to a transmission line. In a transmon qubit, owing to its weak anharmonicity, a single driving field may generate dressed states involving more than two bare states. We confirmed the formation of three-state dressed states by observing all of the six associated Rabi sidebands, which appear as either amplification or attenuation of the probe field. The experimental results are reproduced with good precision by a theoretical model incorporating the radiative coupling between the qubit and the microwave.