Inaccurate BandGap measurement
There are two big sources of error you do not appear to have considered- the reference voltage (your USB supply voltage), which could easily be low by 2%, and the ADC error, which is of the order of 2-4LSBs. Since you're only using the lower 20% of the ADC range, that represents a relatively large percentage error of 1-2% of reading. Averaging many readings does not reduce either of those errors.

Also your number of 266.5 does not make sense with a 5.000V reference. 226.7 would be expected from your calculation and 222.6 as the nominal exact value with a 5.000V reference and a 1.087V input.