Hi! I don't know if this what I think is right. Brownian motion has two very important properties, it has stationary increments and independents incremenets. And it means that increments does depend only on length of interval. So in my opinion
E(B(t1)*B(t2)*B(t3)) = E(B(t1)*(B(t2-t1)+B(t1))*(B(t3-t2)+B(t2-t1)+B(t1))
as I said, Im not sure of it, but in my opinion it looks ok.
do you know how to solve it?