If you want to remove the beginning and end lines as well, you can do this as a one-liner, editing the fields in place:

perl -nie "print unless /begin/../end/" file1 file2
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Of course, the details of quoting, etc. are up to your shell (like for instance, you'd use " instead of ' under Windows shells).

If you want backup files to be made, do this:

perl -ni.bak -e "print unless /begin/../end/" file1 file2
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This will make backup files that are named file1.bak and so on.