cBioPortal imports those files automatically from the latest run of Broad's Firehose: http://gdac.broadinstitute.org/runs/
From there, it is really easy to get those files, for example: http://gdac.broadinstitute.org/runs/analyses__2013_09_23/data/GBM/20130923/gdac.broadinstitute.org_GBM-TP.CopyNumber_Gistic2.Level_4.2013092300.0.0.tar.gz
Or simply, you can use firehose_get tool to download them in batches: https://confluence.broadinstitute.org/display/GDAC/Download
I would usually download copy number data from the HTTP FTP:
For example, here is where you can find copy number calls for colon cancer samples (COAD) from Affy SNP arrays:
It is a bit confusing because the publicly available data contains copy number and not SNP calls.
You may be able to get access to more data with special permission. For example, the files are not labeled as you describe above. See below for access information: