Well, that depends. To get 1TB of cloud space, you will have to pay some monthly or yearly fees. There are no free lunches for it.
My best recommendation would be Google Drive. This link is of a resource I found very useful. It shows how to use google drive for website testing.
This was a web-designers point of view.
Otherwise also, google drive offers upto 3 TB of space (max. I could find). It is also available on all paltforms like iOS, Android, Mac, PC, Linux, etc.
Google drive is the perfect fit for you.