Actually... it's complicated. They're officially "totally absolutely may-a-Zentradi-stomp-us-flat-if-we're-lyin' not nukes", but instead "Reaction weaponry" that just happens to behave like meganukes (possibly antimatter weapons), because apparently up through at least the '80s Japanese TV had an informal taboo on having good guys use actual nuclear weapons (give ya three guesses why...) or at least that's what I've heard. Apparently they were intended to be nukes, but they were renamed so as not to run afoul of that taboo.
actually the arm weapons were just large missiles, usually seen used for surface to air or artillery type roles.
the "i can't believe it's not nuclear" weapons it fired were fired from the
artillery cannons on the back, which were fluffed as 400mm weapons. just a hair short of the 16inch guns on a battleship. since the Iowa's used to have 16inch nuclear shells (the
15-20kiloton yield W19) this isn't actually all that unbelievable.