Final answer:
The band that exemplifies American hard rock and performed at Woodstock, influenced by Cream, is most likely Mountain. Woodstock was a key cultural event of the 1960s, symbolizing a generational shift towards freedom, rebellion, and music.
Step-by-step explanation:
The band you are referring to that performed at Woodstock and is a good example of American hard rock, heavily influenced by Cream, is likely Mountain. Woodstock was a pivotal moment in the 1960s that embodied the cultural shift towards freedom of expression, rebellion, and the promotion of peace and love. It brought together a vast number of people who celebrated music and communal living, making it the cultural touchstone for the generation. Mountain, known for their song "Mississippi Queen," was one of the hard rock acts to grace the Woodstock stage, serving as an exemplar of the hard-edged American rock sound that had emerged during the era.