Does cesarean take the throne after Cleopatra's death?

Yes and no. Caesarion, or Ptolemy XV as he is properly named, was co-ruler with Cleopatra and had been since his infancy. As he grew into manhood, as the male, he was considered the king, even though his mother supposedly made the decisions and gets all the historical hype. So he had the throne all along and for a brief time was the sole ruler.