How does Lincoln use repetition in his speech? What effect does this achieve?

Repetition. Repetition is used to make ideas and points more memorable and create a more appealing sound effect. For example, the speaker uses the word “here” seven times in the speech to emphasize the importance of the Gettysburg battle for the Civil War. :)

Lincoln had a big enough vocabulary to not repeat himself, but using "we cannot" lent the sentence a more poetic structure and tapped into humanity's subconscious appreciation of the rule of three. They help develop rapport and create a sense of “togetherness”.

to extend a country’s power and influence