How did Iroh manage to escape from the prison when the sun was black? As we know the sun got black in E11S03 "The Day of Black Sun, Part 2: The Eclipse".
I believe he waited until all the fire-benders were weak and busted himself out, but how did he manage to do it when he can not fire-bend, or does he have another way to fire-bend without the sun?
We see in the prison that he manages to destroy the metal like it's nothing! So, why can't Mako do the same when he was in the prison with Bolin?
The best we get is the guard proclaiming “He was like a one-man army!” and a visual of snapped and bent cell bars.
My Opinion
Iroh presents himself with a very unassuming manner that makes it easy to forget that he is one of the most martially powerful and intelligent people alive.
I suspect that he began manipulating the integrity of the bars with fire long before the eclipse. Low-level heating makes them malleable to the point that they will bend and break just like you see in the episode. (Imagine if the bars were built out of metal the tensile strength of cheap metal tableware.)
When the time came, he burst the bars by either fire bending them immediately before the eclipse took effect or by sheer brute strength. Either way, the guards would have been unprepared for this, even if they were present in his cell at the time. Dealing with the unprepared and under-trained guards after that was only made more difficult by doing it without killing them.
I personally suspect this is one of the reasons he chose the time of the Black Sun to do it as well. By removing fire bending, he removed the single most deadly variable from the equation.
That, and fire benders are typically not very good martial artists when they can’t fire bend. It is even given several times in the series that fire benders rely too much on the fire itself. In that same episode, recall that palace soldiers went from “We’ll never give up!” to complete submission once they realized they couldn’t bend, and even the army took steps to retreat and save fighting for only when they had bending.
Alternately
Of course, my personal opinion presumes some semblance to reality in the details. The other possibility is the obvious super-human nature of a television program about super-human people, where Iroh DBZed it up and bust through those rails with his immense, super-human strength.
It's pretty simple. Iroh was a master at hand to hand combat. All bending uses a forms of fighting. And since he studied all four Nations, he could simply fight the guards using his newly fit body. Plus not all members of the Fire Nation's army are benders.
Iroh was a general so he new how to plan. He could have taken the Earth Kingdom if his heart was in it. If you pay attention most powerful firebenders are lean but muscular. Most powerful Earth benders are bulky. And so on. So he was a very bulky muscular man fighting lean men who only knew bending or one fighting style.
My Opinion and personal fan theory:
I really like Duthomhas' answer, but he forgot to mention that Iroh was also extremely spiritually strong in contrast to nearly all other firebenders of his day. In prison, Iroh has an epiphany. Knowing that Azula has compromised the security of the Earth Kingdom, he realizes that it really is his destiny to conquer Ba Sing Se after all. During his meditations, he makes a one time deal with the Lion Turtle Spirit of Earthbending-- if the spirit helps him break out of his cell, he will liberate the Earth Kingdom. As an offering of his sincerity, Iroh completes rigorous calisthenics, dedicating every available moment to his displays. He often practices the same routines and forms as the great Earth Kingdom master warriors he once fought long ago. He also spends time mimicking the behavior of Badger moles. When the moment comes, right as the eclipse starts, the Earthbending spirit grants him a singular opportunity to Earthbend, or more specifically metalbend, out of his cell. After succeeding in busting out he can no longer metalbend. Fortunately, having been physically prepared he quickly defeats the warden and guards in hand to hand combat and eventually completes his promise.
