I think Rolf's answer is better than this one as it more clearly explains why you were getting the octal interpretation, but here is a quick one liner to do what you want.

Here I am using autosplit mode with the field separator set to the empty string and using reduce from List::Util:

$ perl -MList::Util=reduce -wlF'' -e 'print reduce { $a + $b } @F'
321023
11
321
6
023
5
[download]

With this technique you can just type your numbers at the command line like I have here, or you could put all your long ints into a file separated by newlines and pass it to Perl as the first argument.

Update: After reading AnomalousMonk's post below, I realized using reduce here is a bit silly. With sum, the code is even more simple:

$ perl -MList::Util=sum -wlF'' -e 'print sum @F'
[download]

Best,

Jim