Watch the difference between coefficients of drag (or lift) and the actual values for drag and lift.

The coefficient of induced drag is proportional to the square of the coeficient of lift.

This is because the more lift you need the greater the downwash and all the other factors that generate induced drag.

Now write angle of attack in place of the coeficient of lift, and consider level flight.

In level flight, from the lift formula, as you speed up alpha goes down, proportionally as the square of increasing IAS. But the “coefficient” of induced drag is proportional to alpha squared, and as alpha is decreasing as the square of IAS the coefficent of induced drag is decreasing as the fourth power of IAS.

But the actual induced drag is the coefficient times the square of increasing IAS, and this now makes the actual induced drag decrease as the square of IAS

So with the IAS doubling in level flight the coefficient of induced drag, Cdi, is down 1/16, but the actual induced drag is down 1/4.