Can 8gb RAM support Intel Pentium dual core 2.7ghz

I think you have your question backwards. It's not "can the ram support the cpu", it's the other way around.

But the question requires FAR more detail. I'm assuming you already have the ram. What type/speed is it? DDR3? DDR4? 1600MHz, 1866? etc.

Every modern CPU is 64bit, and only 64bit CPU's can support more than 4GB. You didn't provide a model number, so I can't confirm if it is 64bit or not.

More info needed.