I want to know whether the torque required by motor depends on load. If it does, then how can I calculate it?
Yes you can find required torque of motor if you know the load. Torque created by the load acts on the motor shaft and the motor shaft must overcome that torque to operate, otherwise it would cease to rotate.
For no load conditions there is a no load amp draw. This represents the internal losses of the motor (bearing friction, major and minor losses) that, at a minimum, the motor must overcome to operate at its design speed.
The torque required by the motor is the sum of different actors, for instance it can be the friction in the motor ($T=K_f \dot \phi$), the inertia of the rotor itself ($T=J\ddot \phi$) and then all the loads connected to the motor shaft. You have to include the inertia as well as the damping and stiffness between the different loads.
Yes, motor torque depends on load. More the load torque more the torque produced by motor. Yes, as previously mentioned answers every motor have some losses, that may be friction losses etc, and at no load the motor will produce a torque equal to the torque due to loss. So the some of Torque produced = Load torque + Torque (friction loss). The torque is not a thing that you can calculate that it will produce. There is a torque-speed charaterstic curve of different motors(dc series,parallel etc) in which it shows how the motor speed changes as you add load on it.