"Now is the judgment of this world: now shall the prince of this world (νῦν ὁ ἄρχων τοῦ κόσμου τούτου) be cast out" (John 12:31)
"Hereafter I will not talk much with you: for the prince of this world cometh (ἔρχεται γὰρ ὁ τοῦ κόσμου ἄρχων), and hath nothing in me"(John 14:31).
"Of judgment, because the prince of this world is judged (ὅτι ὁ ἄρχων τοῦ κόσμου τούτου κέκριται)." (John 16:11).
All biblical quotes from the KJV.
Do these texts have any bearing on our understanding of 2 Corinthians 4:4?