Are there any types of cancer that cause neurons to divide?
I think that most mature cells do not divide in all tissues. If an organism needs to repair tissues, it uses tissue cell precursors -- stem cells. 

In case of neurons, these are neuroblasts. Neuroblasts can divide and can repair brains under some circumstances (I don't know under which). 

There is a cancer grown from neuroblasts, called neuroblastoma.

I think it is very improbable to have tumor from neurons, because division genes are turned off in mature cells. Can't state it is not occurring in practice.