What is the exact part of the brain that does not have pain receptors?
That depends on exactly what you are referring to. The brain itself is loaded with “pain receptors”, that is, neurons tha respond to peripheral sensory neurons that are responsible for reporting painful stimuli. The brain itself does not sense pain, technically, the brain lacks nociceptors. However, pain cognition and modulation is processed extensively in the brain. Additionally, many of the receptors that respond to pain medication are located in the brain and there alteration of function by medication plays a large part in pain perception.