Cancelling a subscription on CORE is fairly straight-forward, the first step would be to log in as the customer and go to Account, follwed by Subscriptions, then clicking on the relevant subscription that you wish to cancel.
From here, you will then see the Cancel Subscription button.
Once cancel subscription has been clicked, a confirmation box will appear asking for a reason and a comment, once entered you can click proceed - if there are any problems or you are unsure please contact firstname.lastname@example.org.
In order to cancel an entire customer account, the use of Classic Panel is required - which can be accessed via the highlighted button in the screenshot below from the reseller homepage.
Once in classic panel, you'll want to switch to Billing view - again highlighted in the below screenshot.
Once in the billing view, select Customers on the left-hand side, find your customer from the list (search if needed) and click on the account name hyperlink. This should take you to the 'General' tab for that customer as shown below.
Scroll to the bottom of this page and you should see a Cancel Account button - if you cannot see it please contact email@example.com as it may be that your admin account does not have permission to do so.
In the same way as cancelling a subscription, it will ask for a reason and a comment before confirmation. Enter these details and click Place Cancellation Order and that should complete automatically.
Please note that finishing this cancellation process will also cancel any active subscriptions that the customer may have.