How can I show syntax-highlighted Python code in a HTML-page?

If you wish to only display code, python in this case, consider using Github gist.

You can then embed it using the 'embed' option on the top right corner. It will give you a script tag that you can copy and add to your webpage like so:

<script src="https://gist.github.com/username/a39a422ebdff6e732753b90573100b16.js"></script>

I use prism.js

It looks Like this, it has many features