Yes, it is relatively easy using the php include or require function. 1. create text file containing the HTML for your menu, i.e. <ul><li><a etc. 2. Save this file as e.g. menu.html 3. In the pages that will use the menu use the following tag instead of the menu: <?php include ('menu.html');?>
require() and include() are identical in every way except how they handle failure. include() produces a Warning while require() results in a Fatal Error, i.e. if your menu file is not found it won't load the whole page.
You don't really need any PHP, use the html #include command. For example, save your left links code section as leftlinks.html, and use a command like <!--#include file="leftlinks.html" --> at the point in the page where you want it to appear.