This Moroccan Hanukah song is sang to the tune of E'eroch shir tehila, which is sung whenever there is a Berit Mila. I believe the reason R' David Bouzaglo composed words to this tune was because the Greeks decried any alteration of the human body and decreed that any form of circumcision would be prohibited. So many years later, the Greeks are gone and we're still around performing the ultimate covenant of God.
Following the piyut, I sing the Kadish using the same tune. I would normally sing this Kadish for Friday night on ליל שבת. After that I would switch into the traditional Maoz Tsur. Although they are totally different maqamim, the congregation is eager to hear Maoz Tsur so I sing the latter half of the Kadish in that melody.
The maqam of this song is maqam Hijaz.