DC analysis of Darlington pair
I think Vbe of Q1 is equal to Vbe of Q2 which is 0.7 volts, so the
  voltage drops about 0.7 volts through each transistor, like Q1(E)
  equals to 8.8 - 0.7 = 8.1 as shown.


No, it's not as simple as that. If you look at the data sheet for the 2N2222 you will see that the base emitter voltage might be as high as 1.3 volts for a collector current of 150 mA.

But it's all a bit hit and miss with the 2N2222 transistor because there are no graphs in the data sheet that could give typical values that are representative of actual circuit conditions. What can be said is that assuming a forward voltage of 0.7 volts for either transistor's Vbe is overly simplistic. It will be greater and quite possibly nearer to 1 volt for each transistor.

Also, worth pointing out is that the simulation tool that predicted 6.59 volts is subject to some speculation. The model it uses will have inaccuracies and these might slightly compound the "true" analysis.