Is Power consumed by a motor under various load conditions constant?
Don't let inductive current lag (apparent power) confuse the issue.  Ohm's law still applies.

When you apply a voltage to a motor, the resulting motion generates a "back ElectroMotive Force" against the coils; its rotation feeds back a resistance that regulates the current, in proportion to the motor speed.

If an external load reduces the speed of the motor, that "back emf" is reduced (the resistance of the motor decreases), increasing current in order to maintain the voltage, and thus power increases.