Error: Failed to build gem native extension when trying to download Rubocop

Do sudo gem install rake and then do sudo gem install rubocop again and it should work.

It doesn't seem to matter that you have the right version of rake installed. For me rake --version reported 10.5.0 but I was still getting the same error message as you.

Looking at the error message, it is looking for rake at a specific path, not just anywhere on my PATH:

/usr/bin/ruby2.3: No such file or directory -- /usr/share/rubygems-integration/all/gems/rake-10.5.0/bin/rake (LoadError)

which rake reports /usr/local/bin/rake, not /usr/share/rubygems-integration/all/gems/rake-10.5.0/bin/rake.

And in fact, as the error message says, there is no file at /usr/share/rubygems-integration/all/gems/rake-10.5.0/bin/rake.

This is probably to do with rake having been apt-get installed rather than gem installed. sudo gem install rake creates that file.

I was able to resolve this problem with

sudo mkdir -p /usr/share/rubygems-integration/all/gems/rake-10.5.0/bin
sudo ln -s /usr/bin/rake /usr/share/rubygems-integration/all/gems/rake-10.5.0/bin/

See this commit on GitHub.