Is it possible to add a
Content Editor Webpart to a SharePoint 2013 MySite-Blog?
If yes, how?
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It is possible.
The default Edit page -mode allows you to add web parts to the page. If you wish to do this on a larger scale (not just for individual page on a blog site), you should do this for a copy of the default page layout. Further guidance available e.g. here: http://josharepoint.com/2014/07/14/dealing-with-style-the-sharepoint-2013-blog-template/