Compress on the cloud, download archive

I have a folder that contains mixed media (e.g. raw research data, images, text & binary files). It has thousands of files, and is over 600 GB in size (it contains my PhD thesis work). I would like to:

a) Generate a compressed file, of archival quality (e.g. tar.gz), on the cloud

b) Download the archive so I can back it up off-line

Is there a mechanism to do this? I do not want to download the whole shebang as my disk drive is not big enough, and temporarily moving the Dropbox folder to an external disk-drive is discouraged. I want to host my own copy, as my access to Dropbox is currently provided by my academic institution, which may change in the foreseeable future.