Here it says that Leviyim carried the Aron. In Melachim I, 8:3 it says that Kohanim carried it!
'Rashi' (5): Verse 5 explains that the 'Leviyim' were Kohanim. Also Kohanim are from Levi! Radak - in 24 places the Kohanim are called Leviyim; one of them is (Yechezkel 44:15) 1 "veha'Kohanim ha'Leviyim Bnei Tzadok" (Yevamos 86b).
Malbim: (Normally, Leviyim carry it.) Chazal counted three times when Kohanim carried it; one was when they entered it into the Kodesh ha'Kodoshim 2 . Sefer Melachim discusses that; here it discusses from Ir David [to the Mikdash; Leviyim carried it].
Radak did not say that verse 5 is one of these places due to the way he explains it (refer to 5:5:5:2). (PF)
I did not find such a text in a Midrash. (PF) Sotah 33b - in three places, Kohanim carried it ? when Yisrael crossed the Yarden, when they surrounded Yericho, and when they returned it to its place [when David fled from Avshalom ? Radak, Melachim I, 8:4. Why did they not count entering it to the Kodesh ha'Kodoshim? Perhaps it is included in 'returning it to its place.']


