Sub Band DFT response With a DFT lets say I had a signal occupying 0Hz to 2048Hz and i am using 2048 bins. 

Can a DFT by design (say FFTW) only calculate the responses in a Sub Band like 768Hz to 1280Hz or -64Hz to -256Hz with the same number of bins?

To put in a context im using FFTW for a project.
Generally if you want to use the same number of bins for a sub-band you should increase the length of the FFT accordingly. That is, say you sub-band width is $BW \;Hz$, then you should increase the FFT length by a factor of $2048/BW$. However, as you can see, this only works if $2048/BW$ is a power of $2$, for example in the first case you mentioned ($768-1260 Hz$). Otherwise, it would required resampling of the signal.