Bookworm,
If we hold pressure altitude and temperature constant then the relationship between CAS and TAS is also constant. Under these circumstances it is true to say that power required is proportional to CAS cubed just as much as it is proportional to TAS cubed.
But if we wish to consider real world situations where pressure altitude and temperature change, the ratio of CAS to TAS changes. Under these circumstances it is more useful to say that power required is proportional to TAS cubed.
To illustrate this let's use msl and 40000 ft in the ISA. At msl the CAS equals the TAS. At 40000 ft the CAS is about half of the TAS. If we climb from msl to 40000 ft at any given CAS the CAS cubed will be unchanged but the TAS cubed will be 8 times its original value.
The power required will in fact only have increased to twice it original value because the density will be about 1/4 of its msl value. Under these circumstances it would be reasonable to say that power required is proportional to Cd x density x TAS cubed. But it would not be at all accurate to say that power required is proportional to Cd x density x CAS cubed.
In summary if we keep pressure altitude and temperature constant, then power required is proportional to CAS cubed in exactly the same way that it is proportional to TAS cubed. But if we want to allow for changes in altitude and density we must use TAS cubed.
Hawk,
I think that I can see what you are saying, but again you are starting with a false assumption. Thrust will not remain constant as temperature increases. It will decrease, causing excess thrust and climb performance to decrease. I suspect that you are using the fact that very high exhaust speeds do not suffer much of an acceleration reduction for each knot of TAS increase. But they still suffer this to some extent. Although we might imagine that the old pure jets would benefit from this effect, they did not do so. This is partly because they did not enjoy the benefits of flat rated engines and partly because increasing temperature reduces thrust in all aircraft propulsion systems (jet or prop).