can I use the html code highlighter from the browser to my website HTML code color "Inspect element" window code color without any plugins like codemirror?

can I use the html code highlighter from the browser to my website HTML code color "Inspect element" window code color without any plugins like codemirror?

Yes: all browsers have some kind of inbuilt developers tools that let you inspect a website's HTML, CSS and other components. The shortcut and method for activating them is different for each, but all of them have a 'highlighter' that allows you to click an element on the page in order to inspect it.
Read more here on using developer tools in all broswers -> http://devtoolsecrets.com/
Chrome's developer tools are arguably the most widely known, commonly used and most powerful. Shortcut is SHIFT + CTRL + J.
edit: in light of the comments below, it looks like OP is after a specific feature of Codemirror that lets you highlight syntax. This is not possible natively in browser.