Is CubeCart compatible with WordPress?

CubeCart has no direct integration with WordPress. Saying this it can work great along side it and many websites are powered by a number of different solutions for different tasks. 

A typical example may have a sitemap like;

Solution Type	Solution Name	URL
eCommerce Store	CubeCart	http://www.example.com
Blog	Wordpress	http://www.example.com/blog
Customer Service Helpdesk	Kayako, ZenDesk, …	http://www.example.com/support

To bring these all together it would be possible to add a shared navigation to each one and even tailor their themes to match. 

What if I want to use a system hosted by a 3rd party and keep my domain name?

Say for example you have a web hosting account that you want to use with CubeCart and a hosted blog or helpdesk which is on a different server or cloud somewhere else in the world. You can get around this by using DNS to point subdomains of an existing domain to point to them.

A typical example may then look like;

Solution Type	Solution Name	URL
eCommerce Store	CubeCart	http://www.example.com
Blog	Wordpress	http://blog.example.com
Customer Service Helpdesk	Kayako, ZenDesk, …	http://support.example.com

Please note that the solution names provided are just for example. There are a great deal of solutions available.