The XSEDE platform: https://www.xsede.org/.
This platform is free of charge. XSEDE has Gaussian16 already installed (at least on the Comet resource), you can ask the XSEDE staff to add you into the Gaussian group once you are in the system, then you can use the Gaussian16 there. XSEDE also has also other software such as AMBER and Q-Chem installed.
If you have not used the XSEDE platform previously, you can write a start-up request for XSEDE: https://portal.xsede.org/allocations/startup.
After you using up the start-up allocations, you can submit a formal allocation application: https://portal.xsede.org/allocations/research. There are relevant Webinars available: https://portal.xsede.org/allocations/research#webinar.
Education application option is also available for education purpose: https://portal.xsede.org/allocations/education.
The Open Science Grid platform: https://opensciencegrid.org/.
The Open Science Grid (OSG) is also free of charge. But in OSG you can not run very long jobs because it is like a scavenge platform for many computational resources. And on this platform, you need to install your own software. I am not sure whether you can install Gaussian there or not because Gaussian is commercial software. But I have consulted their staff and got that you can install computational chemistry software which is free of charge such as ORCA and run it there.
Support home of OpenScienceGrid: https://support.opensciencegrid.org/support/home
Cloud computing service, e.g. the AWS option: https://aws.amazon.com/.
This is a video for how to use AWS EC2: https://www.youtube.com/watch?v=kjrKDtxAZpE (there are more videos available on Youtube). But for AWS, it will take time to be familiar with the system and you may need to install the software by yourself.
The WebMO platform: https://www.webmo.net/
The Chem Compute Website: https://chemcompute.org/
The Mercury Consortium: http://mercuryconsortium.org/