The structure of the two systems' databases is very different, so it's not an easy task to bring existing data (such as product info, customer names, addresses and order history) across from cube to zen.
My advice would be this - so take it as a SUGGESTION, not a GOSPEL !
Get your zen store fully set up as you would like it to appear. Install with DEMO products
Install the EASY POPULATE mod.
Using easypopulate, export the zencart demo product database as a tab-delimited file to your hard drive. This will enable you to see the dbase table headers when you open the file in MS Excel. Keep the column headers, but delete all the demo product data underneath the headers.
In CubeCart, EXPORT the product data (probably best to do this using phpMyAdmin, and as a excel or csv file).
See if you can re-arrange the cubecart data to comply with the data arrangement in the zencart easy populate spreadsheet. Follow easy-populate instructions for uploading the tab-delimited txt file of products into your zenshop.
This will at least enable you to get your product data into your zen store.
Easy Populate cannot be used to port over your customer data. You may have to manually add all your customers or invite them to sign up a-new in your zen store.
Getting past orders from your cubecart into zencart is equally difficult, and may not be worth the challenge.