From the Super Mario Wiki
The Adventures of Super Mario Bros. 3
Large-sized Paragoombas are shown once in The Adventures of Super Mario Bros. 3 episode "Princess Toadstool for President". Bowser and Cheatsy had brought a cage full of Giant Land Paragoombas to the Mushroom Kingdom, whom they unleashed on a field of crops. However, Mario and Luigi showed up and made quick work of the Giant Land Paragoombas, stomping them as if they were standard Paragoombas. They were named after Giant Land.
Super Mario Galaxy 2
Big Paragoombas make their game debut in Super Mario Galaxy 2, in the Supermassive Galaxy. The only way to defeat them is to spin and then kick or spin into them again, as if they were standard Big Goombas.
Puzzle & Dragons: Super Mario Bros. Edition
Big Paragoombas appear in the RPG/puzzle hybrid in Puzzle & Dragons: Super Mario Bros. Edition as stronger variants of Paragoomba. They are of Wood and Light types. A Big Paragoomba's maximum level is 99, and its HP and RCV ratings are higher than those of a normal Paragoomba, although it has the same Attack stat. Its skill, "Rush", deals 50 Wood damage to all foes, and its helper ability is "Attack Boost", which raises the attack of the player's team members.
Super Mario Maker
In Super Mario Maker, the player can enlarge Paragoombas with Super Mushrooms, and they would become, as one can assume, Big Paragoombas. The same result can be obtained if the player attaches wings to Big Goombas. This game marks the debut of large-sized Paragoombas in 2D Mario titles.
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