The youngest of six children, he came from a family of builders but as a gifted pupil he was allowed to visit the Gymnasium in Rastatt.
In 1854 he joined an episcopal ordinariate overseeing educational issues, which had become one of the Church's points of conflict with the government of the Grand Duchy of Baden in Karlsruhe.
After von Vicari's death on 14 April 1868 the cathedral chapter elected Kübel the archdiocesan administrator.
However, the church and the secular government of the Grand Duchy could not agree on a new bishop, so Kübel remained in post until his death, essentially continuing the church-state policies of von Vicari.
Some key issues involved were removing elementary schools from church control, introducing compulsory state exams for theology students, registering births, marriages and deaths in church-run registry offices, making state law superior to church law (a measure completed on 1 February 1870), closing church-run societies, charities and hospitals and only allowing religious charities which were exclusively religious in their purpose.