Try to execute/run the code "npm install -g bitcore" by adding sudo"root privileges" because it will solve most of the permissions problems.
You can check this link for more information ------>
https://docs.npmjs.com/misc/scripts#userIf npm was invoked with root privileges, then it will change the uid to the user account or uid specified by the user config, which defaults to nobody. Set the unsafe-perm flag to run scripts with root privileges.
If this doesn't work with you, try this "npm install -g --unsafe-perm=true bitcore" source ---->
https://github.com/bitpay/bitcore/issues/1458