Does two lines count?
awk '{ sum += $1; }
END { print sum; }' "$@"
You can then use it without the superfluous 'cat':
sum < FileWithColumnOfNumbers.txt
sum FileWithColumnOfNumbers.txt
FWIW: on MacOS X, you can do it with a one-liner:
awk '{ sum += $1; } END { print sum; }' "$@"