Answer:
The way you would answer that question depends on your perspective. An American might argue that the Soviet Union was primarily responsible. A Russian might argue that the United States was primarily responsible. Personally, I'd argue that both bore responsibility for the Cold War's realities.
If this is an essay question, you'll need to pick your own answer and provide reasons in support of your thesis.
Explanation of my answer:
The Cold War came about because of dramatically different worldviews held by the United States of America and the Union of Soviet Socialist Republics. The USA was committed to capitalism and democratic institutions of government. The USSR was committed to communism and imposed authoritarian government. The Cold War was mostly a tension between these worldviews.
There also were immediate issues in the aftermath of World War II that drove the USA and USSR from being allies to being rivals. The USA had atomic weapons and the USSR did not. The US would not share that technology with the Soviets, although they had been allies during World War II. By 1949, the USSR developed and tested the first of its own atomic weapons, and the Cold War rivalry became a nuclear rivalry.
The two countries were also at odds over how governments in Europe would be reconstituted after World War II. The USA wanted free and fair elections and democratic countries to develop, whereas the Soviet Union was looking for governments in Eastern Europe that would align with its communist system and provide a security buffer against what it saw as capitalist imperialism.
So there are reasons to see both sides playing an equal role in the situation that became the Cold War.