In the sentence, “He is being nice”, the word ‘being’ is the present participle
In the sentence “Being ill is really unpleasant”, the word ‘being’ is a gerund.
A gerund looks like a verb, but acts like a noun. We can follow the verb ‘like’ with either an infinitive or a gerund:
I like to go the beach in the winter
I like going to the beach in the winter