Does a land with an activated ability that produces mana count as a mana ability even if it has a cost?

An activated ability is a mana ability if it meets all three conditions in CR 605.1a: (1) it is an activated ability, (2) it is not a loyalty ability, and (3) the ability could produce mana as part of or as a result of its resolution. The presence of a cost does not disqualify it.

This is important because mana abilities are handled differently from other abilities: they do not use the stack (CR 605.3a), meaning players cannot respond to them. They simply resolve immediately when activated. This is true regardless of whether the ability requires paying mana, tapping, or some other cost.

The classic example is a land like Llanowar Reborn or any basic land — tapping a Forest ({T}: Add {G}) costs the tap, yet it is still a mana ability. More complex cases work the same way: a land with an ability like '{1}, {T}: Add {G}{G}' still qualifies as a mana ability because it could produce mana upon resolution, even though it requires paying {1} as a cost.

The only relevant exception is if the ability has a targeting requirement or is a loyalty ability — those disqualify it from being a mana ability (CR 605.1a). A simple cost, however, is irrelevant to the classification.

So in practice: if your land says '{2}, {T}: Add {C}{C}{C}', it is a mana ability. Activating it does not go on the stack, and opponents cannot respond with instants or other abilities between your activation and its resolution.