VFD Power Savings physical explanation - cubic vs square relationship
You are looking at the wrong end of the system. Instead of looking at the electrical end, which only supplies the power+losses to make the motor do what you ask it, look at what you are asking the motor to do.

If the motor is driving a fan, or driving an impeller churning any Newtonian fluid, where the torque varies as the square of the speed, then the power rises as the cube of the speed.

If the motor is driving a winch, say in a crane, then when lifting a weight, the torque required is independent of speed, the power will vary as the speed.

Two different types of load, two very different scaling laws.

In any real case, the detail will be more complicated than a pure 'scale speed raised to a power' law, but this covers the gross behaviour. You have to measure your load, and see what it does.