Is there a way for me to copy an entire database in cPanel?

Go to cPanel > MySQL Databases and Create a New Database with the name you want.
Go to phpMyAdmin and in the left menu click the original database you want to copy (do not click on any tables inside).
Look to the top tabs and choose Operations.
Enter the new database name (full name e.g. username_databasename) next to Copy database to: and uncheck “CREATE DATABASE before copying”. Only “Structure and data” should be selected.
Note: You cannot use Rename database to: because you cannot create databases in phpMyAdmin.
Click the GO button in the same box.