I got the 1.56g/ml number from the internet.
Don't believe everytjhing you find on internet. These are densities in g/L, not mL.
Now, during brewing there is also ethanol produced, so not necesarilly all carbon goes into carbon dioxide.
Note that volume of one mole of CO
2 is 22.4 L at STP (around 0 deg C and 1 atm). Usually you will work at higher temp, so the volume will be higher.