Right, letting the N_3O_6 drop out as nitrogen dioxide,
7*CO_2 + 2.5*H_2O is just 16.5. However, detonation
might not even produce the nitrogen dioxide, and it
might lose energy by producing NO instead of dioxide.
So I'm not sure where the 6 comes from.
Also, the energy from C+O_2 would be much lower than that
from the H_2+O, per O, I think, but I'm not sure how
well defined the combustion process is, that is being
assumed. I think, if detonation in air also entailed
complete combustion, then detonation would
produce the same energy as would direct combustion.
You mentioned something earlier about atomic hydrogen: I
am not sure about this, because combination to H_2 would
just be creation of one covalent bond. Can you explain
further?
The exact amounts of energy involved are all available in the open
literature - that is where I found them, some thirty years ago, and
I'm sure that they are still available now.