Government grants by name, don't have to be paid back. The recipient is "granted" the funds. However, some grants do come with partial loans. Meaning, sometimes the government wants to be paid back part of the money. It's important to study each option carefully to know what you are getting into.
Most government grants are for research but sometimes they will grant funds for education itself.
Here are some United States government organizations that offer both educational grants as well as research grants.
NASA (National Aeronautics and Space Administration:
Applications and descriptions or whats required can be found on one of two websites. Check the Goddard Space Flight Center Grants site or the NASA Shared Services Center.
NIH (National Institutes of Health:
You'll want to check into programs offered by these two branches of the NIH, the Center for Scientific Review and the Office of Extramural Research.
NSF (National Science Foundation):
The NSF grants are primarily for research but it's worth reviewing as they fund 10,000 out of 40,000 applicants every year. Learn more about it at this link.