The Cuban X-Giants were not Cuban, but were former Cuban Giants in large part. They begun to form a rival to that top black team in 1895. Former Giants manager Cos Govern piloted a team which included 2B Sol White and P George Stovey. In 1897 they beat the Giants 2 games to 1 in a series. With E.B. Lamar Jr. at the helm and Frank Grant joining in 1898 the club continued to establish themselves as the new powerhouse in the east. Grant and White left in 1900 and Bill Monroe joined at second base; both the Giants and X-Giants claimed to be the champions, a situation that was duplicated a year later. In 1903 the club boasted Rube Foster on the mound and a middle infield of Charlie Grant and Home Run Johnson. They played in the integrated Tri-State Independent League and then took 5 of 7 from the Philadelphia Giants 5 games to 2 for the title as top black team in the east. Foster won all 4 games in the series and also was 6 for 17 at the plate. That winter, they became the first Negro League team to play in Cuba, meaning that the club with Cuba in its name had no Cubans and their opponents (not so named) were 100% Cuban. Grant and Foster left for Philadelphia after the season and the X-Giants dropped the series the next year 2 games to 1, as Foster was 2-0 against his old teammates. In 1905 the X-Giants became the first black team to beat a Major League Baseball team, when they took 1 of 2 games from the Brooklyn Dodgers, outscoring them 8 to 3 in the process. Pop Lloyd played for the team in 1907, right before it folded for good.
Sources: The Complete Book of Baseball's Negro Leagues by John Holway, The Biographical Encyclopedia of the Negro Baseball Leagues by James Riley, Cuban Baseball: A Statistical History by Jorge Figueredo