Could anyone tell me where the AUX port is located in the 2008 Mazda3 hatchback?

Not all models have it. If there's none under the armrest, you can buy an aftermarket adapter cable and connect it from the back of the radio. There's a reserved socket on the back. Or you can simply replace the radio with an Android large screen unit, and directly sync your phone apps with wireless CarPlay/CarLife/Android Auto. How nice!

Armrest box?