If you are using a CDN all your assets will be delivered directly from the nearest server to your visitors. But your website optimization is still the factor which determine the loading speed.
Because if you are sending not optimized content to your CDN, it will be delivered faster but not optimized to your visitors. So it will require to optimize image by compressing them properly, to combine and to minify the css and the javascript.
And the last factor will be your hosting, but you will not need more CPU or more RAM, but to find a way to reduce the website display processing. For that the most used, and the most efficient is to use a cache solution to limit the queries to your database, and the process of php code to serve static content.
For example, memcache give you the ability to store in memory a static version of your website, to deliver it faster.