From the Super Mario Wiki
Mega Goombas are gigantic versions of Goomba that are bigger than Grand Goombas. In fact, they are the biggest species of Goombas.
Super Mario series
New Super Mario Bros. Wii
Mega Goombas first appear in New Super Mario Bros. Wii. Mega Goombas only appear in the World 1 Enemy Course, where two of them appear trying to stop the player from saving the kidnapped Toad. Mega Goombas share the same attack pattern as many of their smaller relatives. When jumped on, they split into two Grand Goombas. If Ground Pounded, it splits into four normal Goombas. It takes four Fireballs to defeat a Mega Goomba. Mega Goombas can't be frozen by iceballs from Ice Mario; they will break out instantly after being frozen.
New Super Mario Bros. U
Mega Goombas reappear in New Super Mario Bros. U. They act the same like in New Super Mario Bros. Wii, when they are jumped on they split into 2 Grand Goombas or 4 normal-sized Goombas, except they now require three fireballs to take out. They are found in Soda Jungle's course Jungle of the Giants with Gargantua Koopa Troopas. They can be defeated by Koopa Shells now. Additionally, they appear in a challenge called Big Goomba Bounce Bash.
Mario Golf: World Tour
A Mega Goomba appears in Mario Golf: World Tour on Hole 2 of Wiggler Park. Because it appears behind the green, it is unlikely that the player should hit the ball into it. If they manage to do so, it will cause the Mega Goomba to look around wondering what just happened while the player's ball would likely land Out of Bounds.
Mario Party 10
Mega Goomba being fought in Mario Party 10
Mega Goomba makes its first Mario Party appearance in Mario Party 10, where it is one of the game's bosses. Its boss minigame, Mega Goomba's Ladder Leap involves players climbing up to a higher platform and jumping down onto it to deal damage.