In future, please post output in text form rather than screenshots, as text in images can be really hard to read even on desktops.
Based on your
brew config output, you have a older version of gcc (v4.8.5) than the one with which all Homebrew software is built and tested on Linux (v5.5). Upgrading your GCC may well solve your problem, since otherwise you’re building a
binutils that’s five years newer than your compiler.
Also check the log files in
/afs/crc.nd.edu/users/s/swang18/.cache/Homebrew/Logs/binutils to see where and why your build failed (if I typed that path wrong, you now know another reason why plain text is always preferred to screenshots for these purposes). As the first screenshot says, it’s only showing you the last 15 lines of one log file.
Lastly, since you’re installing Homebrew in a non-standard location, official support will probably not be forthcoming.
Sidenote: Despite your topic title, your issue has almost certainly nothing to do with
sudo. Neither builds nor installs of Homebrew formulae involve root, though some formulae may have post-install instructions to perform certain actions as root.