Is the triggered ability of Caged Sun a mana ability or not?
To understand this question we need to first fully understand what a "triggered mana ability" is. This is defined by the following rule in the Comprehensive Rules:
605.1b A triggered ability without a target that triggers from activating a mana ability and could put mana into a player's mana pool when it resolves is a mana ability.The following rule makes it clear when a triggered ability is not a mana ability:
605.5a An ability with a target is not a mana ability, even if it could put mana into a player's mana pool when it resolves. The same is true for a triggered ability that could produce mana but triggers from an event other than activating a mana ability, or a triggered ability that triggers from activating a mana ability but couldn't produce mana. These follow the normal rules for activated or triggered abilities, as appropriate.So, in summary, a triggered ability is a mana ability if it produces mana, does not target, and it triggers from activating a mana ability. If the ability targets, or it triggers from a non-mana ability, then it's not a mana ability even if it produces mana.
(A relevant difference between the two types of abilities is that a mana ability does not use the stack, and instead it resolves immediately when it triggers. It cannot be responded to. A non-mana ability uses the stack and can be responded to.)
So the question is: Is the ability of Caged Sun a mana ability or not? (Does it use the stack? Can it be responded to?) The ability in question reads:
Whenever a land's ability adds one or more mana of the chosen color to your mana pool, add one additional mana of that color to your mana pool.Normally a mana-producing ability of any land is a mana ability, so it fulfills all the requirements for the ability of Caged Sun to be a mana ability.
However, the million dollar question is: What happens if a land has a non-mana ability that produces mana?
There exist currently no land cards that have such abilities. However, it's possible to create this kind of situation via gameplay. (One possibility is to, for example, make Deathrite Shaman into a land while retaining all of its abilities. This is possible by using certain combinations of cards.)
Technically speaking if a non-mana ability of a land produces mana like this, the ability of Caged Sun will trigger and it will not be a mana ability in this case according to the strict interpretation of the rules (and thus will use the stack.) In other words, whether the ability of Caged Sun is a mana ability or not depends on what's triggering it.
This is, as far as I know, not the intent of the card, or the game's rules in general. An ability ought to always be either a mana ability or not, rather than switching between the two depending on the situation. In other words, it ought to be a fixed characteristic of the ability that doesn't depend on anything else.
Probably for this reason the official ruling by WotC is that the ability of Caged Sun is always a mana ability, regardless of the situation (at least as of writing this post.) The interesting thing is that the comprehensive rules do not support this interpretation.
As of writing this post there is no disambiguating rule in the comprehensive rules to settle this question, but many people predict that it might be added there in the future.