What is the advantage of praying inside the Kaaba?

There is no verbal evidence regarding the virtue of praying inside the Kaaba, but the Prophet's (peace be upon him) action of doing so indicates the desirability of performing supererogatory prayers within it. Supererogatory prayers are valid inside the Kaaba and on its roof by scholarly consensus. As for obligatory prayers, the preponderant opinion is that they are valid, but it is preferable to avoid performing them inside the Kaaba to avoid disagreement and to emulate the Prophet (peace be upon him) who performed obligatory prayers outside of it.