1. A cloud computing system providing a virtual private cloud within a public cloud, the system comprising: a plurality of physical servers; a first instance of a cloud-in-a-box deployed to one of the plurality of physical servers a plurality of virtual machines created by the first instance of a cloud-in-a-box; and a second instance of a cloud-in-a-box, wherein each instance of a cloud-in-a-box comprises— one or more adapters configured to manage virtual infrastructure of a cloud, wherein one of the one or more adapters is configured to recognize a instance of a cloud-in-a-box itself as a type of virtual infrastructure, a library configured to store virtual machine images, an end-user portal configured to provide an end-user access to the library, and an admin portal configured to provide management functionality for an administrative-user, wherein an adapter of the second instance of a cloud-in-a-box is communicatively coupled to an end-user portal of the first instance of a cloud-in-a-box.