Add up a column of numbers at the Unix shell

Here goes

cat files.txt | xargs ls -l | cut -c 23-30 | 
  awk '{total = total + $1}END{print total}'

... | paste -sd+ - | bc

is the shortest one I've found (from the UNIX Command Line blog).

Edit: added the - argument for portability, thanks @Dogbert and @Owen.