Bowser's Brother

Bowser's Brother, also referred to as Fake Bowser (Blue) (apparently a mistranslation of the Japanese name "Kuppa (Blue)" from the original page), is a character similar to Bowser who appears in Super Mario Bros.: The Lost Levels. His identity varies in supplemental material, with his most consistent characteristic being his bluish color that was removed in Super Mario All-Stars.

Super Mario Bros.: The Lost Levels
Bowser's Brother makes his first appearance in the Family Computer Disk System version of Super Mario Bros.: The Lost Levels. There, he appears before the fight with Bowser in World 8-4, where he tries to stop Mario or Luigi by throwing hammers at them and breathing fire. He reappears alone in World 9-3, but does not breathe fire.

While distinguished from Bowser by the color of his skin and shell (brown and deep cyan, respectively), defeating him with fireballs does not reveal him as one of Bowser's minions, making him distinct from the fake Bowsers. In World D-4, however, a fake version of him appears that only breathes fire, being revealed as a Spiny when defeated with fireballs.

All Night Nippon: Super Mario Bros. reuses World 8-4 and World D-4 from The Lost Levels, so Bowser's Brother and his imposter also return.

Bowser's Brother returns in the Super Mario All-Stars remake of The Lost Levels, where he is colored identically to Bowser, though an unused color palette shows him with his blue color scheme, as well as magenta hair. In World D-4, he replaces his imposter but does not breathe fire.

Super Smash Bros. series
In Super Smash Bros. for Nintendo 3DS / Wii U and Super Smash Bros. Ultimate, the eighth costume of Bowser is said to be Bowser's Brother in the tips. It replaces a similar-looking costume from previous games that has yellow hair and green limbs, likely based on Bowser's original artwork (though with the shell and skin colors swapped).

Blue-colored versions of Bowser distinct from Bowser’s Brother
Even though these blue-colored versions of Bowser likely affected the depiction of Bowser's Brother, they are not stated to be him.

Super Mario Bros.
In the original Super Mario Bros., the palette used for castle sections before the final boss battle causes an unintended consequence in which Bowser has the same blue coloration of Bowser's Brother. This is due to color of Bowser's skin and shell being obtained through a palette swap commonly used in castle sections of the game, except for the part where the axe is loaded. Because of this, standing near the end of a castle in a way so that Bowser is barely seen on the right-hand side of the screen causes him to appear dark shades of teal, but he will revert back to his correct colors if Mario or Luigi advances any further. The same graphical oversight can be seen in Super Mario Bros.: The Lost Levels. Additionally, defeating a fake Bowser before his color change will result in the enemy acting as his true form to retain this color scheme (such as World 5-4's fake Bowser becoming a Lakitu using the underground/castle color scheme). Similarly, in the Disk System version of the Minus World, due to that level using the underwater color palette, causing all green enemies to turn gray, including the "green" Cheep-cheeps, Bowser appears gray in his appearance in that version of World -1, based on World 1-3.

Mario Golf (Nintendo 64)
The second palette swap of Bowser in the Nintendo 64 version of Mario Golf features a blue skin and a blue shell. Contrary to what would happen in Super Smash Bros. for Wii U, the shell and head have a lighter blue color than the skin.

Mario Tennis (Nintendo 64)
In the Nintendo 64 version of Mario Tennis, one of Bowser's palette swaps features the same blue colors seen in Mario Golf.

Identity
He is initially mentioned as the first/fake or first/blue Bowser in the Japanese guides of Super Mario Bros.: The Lost Levels, which do not specify his relationship to Bowser besides one suggesting that he is not his twin. In the character books of the '90s released before the release of Super Mario All-Stars, the blue Bowser is described as being either Bowser's first or younger brother. Super Mario Zen Hyakka, a book written in collaboration with Nintendo, describes him as part of the「」(Ō-zoku, literally "King Tribe") and thus a leader of the Koopa Troop and member of Bowser's royal family, along with the Koopalings and Bowser himself. Due to his recoloring from blue to green in Super Mario All-Stars, he is not considered a distinct character from fake Bowsers in the Japanese official guide book. Contradicting one of the original Japanese guides for The Lost Levels (which suggested that he was not a twin), when "Bowser's Brother" is described in Nintendo Power's guide for Super Mario All-Stars it states "Bowser's got a twin". After the release of Super Mario All-Stars, he was referred to as a fake Bowser, with the exception being the Prima Games guide for Super Mario Bros. Deluxe, where he is again considered Bowser's brother. In Super Smash Bros. for Wii U, the English text suggests the blue Bowser is a fake while the Japanese version leaves his nature ambiguous. Super Mario Pia, a memorial book also written in collaboration with Nintendo, depicts the blue Bowser as a particular fake Bowser. Encyclopedia Super Mario Bros., which was released around the same time, distinguishes him from fake Bowsers but states that his identity is unknown. The Japanese Mario Portal website similarly lists him as a blue Bowser, while the English version lists him as a blue fake Bowser.

Super Smash Bros. for Wii U / Super Smash Bros. Ultimate tip

 * "A Bowser Impostor?! – In Super Mario Bros.: The Lost Levels, Mario fights a blue fake Bowser before the real thing. That blue fake is his eighth color in this game!"

Trivia

 * Due to his bluish coloration, Bowser's Brother resembles Shigeru Miyamoto's original blue depiction of Bowser in artwork for Super Mario Bros., prior to the character's redesign in artwork for Super Mario Bros.: The Lost Levels.
 * In the speedrunning community for Super Mario Bros.: The Lost Levels, Bowser's Brother is often nicknamed "Bruce".