Early North American and European print runs of the God of War Collection (which bundled remastered versions of GoW 1 and 2 for the PS3) included a voucher code or a direct disc link to access the God of War 3 demo.
It was free during its promotional period (2009-2011). Today, it is no longer distributed for free legally.
The availability of the demo download depends on the platform. Historically, demos for PlayStation games were made available through the PlayStation Store for download. However, the specific steps to download the demo can vary based on updates to the PlayStation Store and the console's software.
Today, if you manage to launch the original demo, you will notice: