For your various compute needs the supercomputing facility at the Zuse Institute Berlin (ZIB) is available. You do not have to be directly associated with the ZIB since it provides its services for external researchers as well.
https://www.zib.de/research_services/supercomputing
If you plan to utilize Jupyter Notebooks for your working group or en educational project just contact the IT and Data Services at ZIB.
Data Repositories
Several Data Repositories for publication of research data are available in the MATH+ Cluster of Excellence. These repositories offer a place for datasets up to a size of ca. 5 GB. You have to be affiliated with the hosting institutions to use their services:
Deposit Once of Technische Universität Berlin
https://www.depositonce.tu-berlin.de
Refubium of Freie Universität Berlin:
https://refubium.fu-berlin.de/?locale-attribute=en
EDOC server of Humboldt University Berlin:
https://edoc.hu-berlin.de/handle/18452/19149?locale-attribute=en
If you have larger data sets, that you want to publish please consult with rdm@mathplus.de