They mean the same, but the emphasis on "do" in the second version could be a clarification. It could be a correction if someone asks "you don't believe?".
They have the same basic meaning. The 'do' in the second sentence expresses a kind of emphasis designed to affirm the statement's truth in the face of other information that may be contrary to it.
For example, two friends are talking about Henry Kissinger.
Person 1: "Do you believe he is a great person even though he is implicated in so many war crimes?" Person 2: "I do be