The way you describe this, it sounds like the fighting had gone on for more than six days the other posters mentioned. Unless your sources know better, I haven't read them yet.
The war had been going since 149 BCE and was brought to an end in 146 BCE. The siege lasted for a long time, to the utter frustration of Rome. Its breakthrough, which started from the moment the Romans managed to enter the city to the eventual surrunder of the citadel, lasted about a week, as @alexmilman pointed out.