He wanted to create a new Roman Empire.
It might be true that they wanted to aid their home country achieve empire. There is the remote possibility that they wanted to create a fishing empire to feed the hungry of the world. Most likely they wanted a successful colony because of the wealth it would produce for them personally.
Taiwan
Japan
With respect, Hitler's key territorial aim was to create a vast German empire in Eastern Europe. (There's no evidence that he wanted to revive the Holy Roman Empire).
Each country had their own reason for entering the war. Germany was pissed that they got screwed over by the Treaty of Versailles, Japan wanted to create an empire (at the expense of the "western" countries), Mussolini wanted to gain from France and Britain. Etc, etc.
Italy joined WW2 because they wanted to create the Roman Empire again. Leading them to ally with Germany and Japan
It was B Mussolini wanted to expand his country to challenge the Soviet Union, but Hitler wanted to expand his country to increase trade with the Soviet Union.
I`m from Germany and i`ve done this in history , he wanted to create a big world-empire. He did not want to call it "Deutschland", but "Germania". He was ill and mad.
If you had the power to rule an Empire, wouldn't you?
Britain
Sargon The Great was the first person in the world to create an Empire.