Yes they can. There are many documented cases in several animal species including dogs, cats and cattle. They were considered rare in humans, but more sensitive diagnostic tools have uncovered several instances lately. You may refer to
@DrPatole: The notion that all brain tissue in the adult human are post-mitotic is now obsolete. Adult neurogenesis has been shown to occur in three primary places of the brain: the dentate gyrus of the hippocampus, subventricular zone, and the olfactory bulb. This means that cancer is possible in these three regions of the brain.
The WHO Classification of Tumors of the Central Nervous System, including the revised 4th edition from 2016, contains a group of Neuronal and mixed neuronal-glial tumors. It includes the following entities: Dysembrioplastic neuroepithelial tumor (DNT), Gangliocytoma, Ganglioglioma, Dysplastic cerebellar gangliocytoma (Lhermitte-Duclos disease), Desmoplastic infantile astrocytoma and ganglioglioma, Papillary glioneuronal tumor, Rosette-forming glioneuronal tumor, Diffuse leptomeningeal glioneuronal tumor, Central neurocytoma, Extraventricular neurocytoma, Cerebellar liponeurocytoma, Paraganglioma. All of these tumors have a component of cells with immunohistochemical and ultrastructural signs of neuronal differentiation. They are mostly tumors of low malignant and high epileptogenic potential.