Profit for something like AWS is likely difficult to put a number on.
They built it so they could run Amazon.com off the infrastructure, but then decided they could make money leasing their under-subscribed portions.
If they are not making a cut-and-dry profit from AWS (I'd fathom they are, they are one of the most expensive cloud providers and many other providers turn a healthy profit), then they are at least dramatically offsetting their own Amazon.com infrastructure costs which are mandatory anyway.
They built it so they could run Amazon.com off the infrastructure, but then decided they could make money leasing their under-subscribed portions.
If they are not making a cut-and-dry profit from AWS (I'd fathom they are, they are one of the most expensive cloud providers and many other providers turn a healthy profit), then they are at least dramatically offsetting their own Amazon.com infrastructure costs which are mandatory anyway.