Songbook – Publish post titles to a page grouped by cat/subcat?

I am looking for guidance on a feature, plugin, or theme to accomplish a solution .

Is there an easy way to build a songbook in WordPress? My thought was having a category of “songs” and then maybe some subcategories of “occasions”. And then each song is a post. What I think I’d LIKE to have… is a Page, that publishes the titles of all the posts of a category to a page, grouped by subcategory. This way a person could easily refer to a page and see all the content from a category and jump to the lyrics.

What I want to avoid, is maintaining the Page and links to the posts! Is this easy to do?