Born in Naumburg in 1890, Hube joined the German army as a volunteer in 1909, serving during the First World War with the rank of Lieutenant. He took part in the conflict from its earliest stages, mutilating his left hand in September 1914 in a battle on the French front. The disability did not prevent him from returning to the front a year later in command of an infantry company. Decorated for valour, he spent the inter-war years in the German army as a Company Commander and Training Officer in Dresden.

With the outbreak of the Second World War he immediately became involved, taking part in the invasion of Poland in September 1939 and, a few months later, in the French campaign at the head of the 16th Infantry Division. After his successes on the Western Front, he was put in charge of the new 16th Armoured Division and transferred first to Romania and then to the Eastern Front, where he was successfully deployed in the Ukrainian sector of Operation Barbarossa.

From there, Hube found himself in the rank of Lieutenant General. Not long after he took command of the 14th Panzerkorps they were involved in the Battle of Stalingrad. As the German situation on the Eastern Front became critical, he was evacuated in January 1943 and sent to the Mediterranean front at the head of a reconstituted 14th Panzerkorps. Transferred to Italy to organise the defence against the Allies, Hube assumed command of the Axis forces in the defence operations in Sicily. From that position he succeeded in slowing down the Allied advance to such an extent that he was able to organise the evacuation of German troops from the island.

After managing the retreat of the German troops following the Salerno landings and setting up the Gustav Line, Hube was once again reassigned to the Eastern Front to try to curb the Soviet counter-offensive. He was then placed in command of the 1st Panzerarmee, which from October 1943 suffered a series of defeats at the hands of the Red Army along the Dnestr river.

On 21 April 1944, Hube was killed in a plane crash on his way back from Hitler's birthday celebrations on the Obersalzberg.