If you create a new database it's good to create user with permissions only for this database (if anything goes wrong you won't compromise root user login and password). So everything together will look like this:
mysql -u base_user -pbase_user_pass -e "create database new_db; GRANT ALL PRIVILEGES ON new_db.* TO new_db_user@localhost IDENTIFIED BY 'new_db_user_pass'"
base_user is the name for user with all privileges (probably the root)
base_user_pass it's the password for base_user (lack of space between -p and base_user_pass is important)
new_db is name for newly created database
new_db_user is name for the new user with access only for new_db
new_db_user_pass it's the password for new_db_user