The Rama in Hinduism seems to be the same person as Raamah (son of Cush or grandson of Ham) in the Bible. In both the Bible and the Hindu texts, Rama and Raamah had two sons. The names of Raamah's two sons, according to the Bible, are Sheba and Dedan. The names of Rama's two sons according to the Hindu texts are Lava and Cusha (sometimes spelt as Kush, Cusha). In the two cases, both characters have two sons. In the two cases, the name Cush is also mentioned, although in the Bible, Cush is the father of Raamah and in Hinduism, Cush is the son of Rama.
Some genetic evidence also seem to link the Raamah of the Bible with the Rama in Hinduism. In the Bible, the descendants of Raamah are purported to occupy the lands surrounding Yemen and the Horn of Africa (Ethiopia and Somalia. Coincedentally, y dna haplogroup T is found in the highest concentrations in the Horn of Africa and in parts of North and East India, including an area near to the ancient city of Ayodhya.
So in conclusion, Rama in Hinduism as well as the Raamah of the Bible could be the same person who can be identified as the ancestor of the first settlers to India, known by historians to be the Dravidians.