where is this cave located?
They are on Elephanta Island, at Mumbai Harbour.
Elephanta Caves
They are on Elephanta Island, or "Gharapuri" (literally "the city of caves"), in Mumbai Harbour, east of Mumbai in the Indian state of Mahārāshtra.
cave temple of elephanta are dedicated to which god It is dedicated to the Hindu god Shiva.
wiki:13269356
Elephanta Caves [SEP] Introduction
Elephanta Caves are a UNESCO World Heritage Site and a collection of cave temples predominantly dedicated to the Hindu god Shiva. They are on Elephanta Island, or "Gharapuri" (literally "the city of caves"), in Mumbai Harbour, east of Mumbai in the Indian state of Mahārāshtra. The island, about west of the Jawaharlal Nehru Port, consists of five Hindu caves and a few Buddhist stupa mounds that date back to the 2nd century BCE, as well as a small group of two Buddhist caves with water tanks. The Elephanta Caves contain rock cut stone sculptures that show syncretism of Hindu and Buddhist ideas and iconography.