why was the reason the soviet union had so much power over eastern Europe?

Huge military, and no compunction about using it.

You prolly mean why Russia had so much influence over eastern Europe. It's because Russia played significant part in liberating Eastern European countries from nazi regime, which was and it is still considered as one of the most brutal regime in history of humankind by eastern Europeans, general speaking.

So Russia ofcourse after the war had a political and military capital to endorse russian interests in those countries.

Liberating ????? ahhahahaaha
They sure didn't do it to be nice guys !
If it was for liberating people, they wouldn't shoot people who tried to escape, and kept the whole country, everyone, not just their chosen undesirables, EVERYONE imprisoned in their USSR with the whole borders in barbed wire, walls and machine guns and vicious-pedigree attack dogs trained for "no mercy", plus the extensive intrusion into personal communications, mail, censorship, illegalizing city maps with dire consequences, disappearance of people without fair trials. It sure was not for liberating anyone from anything !!!!

It was Russian Imperialism to the hilt ! Their beginning at their attempt to get world domination and control. Nothing less. After the war, it included more murders than any other regime in history, including genocide or ethnic cleansing, wiping away any indications of truth of history, and charging ahead with eradicating other cultures and languages, including Estonian, Latvian, and in some areas like Koenigsburg East Prussia even German language, after having been a Teutonic Order of Knights developed town since 3/4 of a millenium. They wiped out books and history and eradicated castles and palaces and any evidences that the place wasn't always Russia, wiped out anyone who would speak the truth, and emigrated a lot of Russian people so it became the dominant language with fatal apathy for the original ethnic people and languages. They spent all their economy on surviving with themselves of course, AND on getting ready to try to take over the rest of Europe, and North America too. They were active at it in the Cuban Missile crises in their beginning strategies to take over America, Russian spies caught in Canada, and they were trying to spread their spores of propaganda, influence, and spread soviet weapons, all around Africa and South and Central America. NATO countries had to always be on guard against any impending attacks and their further attempt at World Domination !!!

the soviets gained all the countries the nazis lost to the soviet union.