Firstly please check with your web hosting company that regular daily backups are made of your web hosting account. You may want to check that this includes everything from the website files and databases to emails and SSL certificates.
To take an ondemand backup of CubeCart in its current state there are two methods.
Method 1 - From your CubeCart Control Panel
If you already have CubeCart setup and working a backup of the database and files can be created from the "Maintenance" section of your admin control panel. If you get no errors please take the time to download both to your local computer and extract any zip archives to make sure they are working and complete.
Please note that this method is restricted by the set PHP memory limit, timeout and web server permissions to read/write files. It doesn't always work. If you do get any error messages or your backups are corrupt please use method two.
Method 2 - From your web hosting control panel
It's not easy to provide exact backup steps here as there are many different hosting control panels with varying functionality. Please either use FTP to download all your store files or (if available) an inbuilt filemanager to creat a zipped archive of your store files. From the MySQL database area you should be able to access a tool called phpMyAdmin which can be used to take an export of CubeCarts database.
How do I know which database CubeCart uses?
You can find the name of the database from the includes/global.inc.php file under $glob['dbname'].