Instructions
Attach a controller to your console and power it on without a disk in the tray, prompting the main menu, known as the Xbox dashboard, to pop up.
Scroll up to "My Console" using the Xbox 360 controller and select "System Settings" followed by "Memory."
Highlight and select the storage device you want to format/erase. In this case, highlight "hard drive" and select it. It should show you how much space is available on the device.
Select "Format" on the preceding screen. This will prompt a warning message to pop up telling you that you're about to delete all of the items on the hard drive. Select "Yes" to confirm the operation. You may be asked to confirm your console's serial number, which can be found on a label on the back of the device. Enter it and press "Done" to continue formatting, which will erase all of the hard drive's data.