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There is no simple answer to the question of whether or not it is possible to use standard backup applications for cloud data. The answer depends largely on the type of data and the cloud where it is stored.
Most off-the-shelf backup applications are designed primarily for backing up the local data center. Many of these products have the ability to back data up to the cloud, but designated features for backing up cloud data are still somewhat uncommon. There are tools (and, in some cases, add-ons) available for backing up certain cloud-based applications such as Office 365, but backing up this type of cloud data presents a number of logistical challenges for backup vendors.
Although there are exceptions, it is generally safe to assume your backup software cannot back up data from an application hosted within a software as a service cloud. However, I expect this functionality to become more common.
Infrastructure as a service (IaaS) clouds are a different story. Large organizations that use IaaS clouds extensively often treat them as an extension of their data center. Typically, a site-to-site VPN provides connectivity between the local data center and the cloud environment. This VPN connection allows for Active Directory synchronization, data lifecycle management and any number of other tasks.
Backing up data residing in an IaaS cloud connected to the local data center through a site-to-site VPN is relatively easy. Assuming the proper permissions and mappings are put into place, backing up cloud data isn't all that different from backing up local resources. The backup software is blissfully unaware that the applications it is backing up are cloud-based because the cloud is treated as a data center extension.
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