I can't insert Padlet Shortcode in my wordpress blog.

From your profile it appears that you have a WordPres.COM blog. Plugins such as this one are not supported on WordPres.COM blogs.

If that’s the case the you’re posting in the wrong place and need to ask in the correct forum.

https://en.forums.wordpress.com/forum/support

This forum here is for self-hosted www.remarpro.com software installations.

This link explains the differences.

https://en.support.wordpress.com/com-vs-org/

It’s a common misunderstanding. ??