If you are just passing through the data from ADC into DAC (so no onboard processing), you might want to check the analog part. I'm not an analog guy (not in a sound spectrum anyway), but I do seem to recall that the voltage on the output depends on the load resistance. I glanced over DAC's datasheet, and it seem to be expecting a fairly high load resistance, especially if load capacitance is also high, so you might want to make sure the load is within allowed range.
Also if you work with a typical line signal of 1 Vpp, you are under-utilizing the ADC range as it's a bit over 0.5 * Vcc, so in your case (Vcc = 3.3 V) it can take up to 1.65 Vpp. Granted, with 24 bit ADCs this is not that important, but if you want to maximize your dynamic range, you might want to boost your signal a bit. Or if you can't be bothered with all of that, just boost your signal in the digital form before you pass it to a DAC as 1 Vpp is going to be quite far away from the saturation.