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Memorize that poem by next week.
Literal
Next-week [by-までに] that poem [object-を] memorize.
~までに ('by [a deadline]') contrasts with the まで — まで is continuous 'until,' までに is a deadline. 暗記する ('to memorize,' literally 'dark-recording') is a suru-verb for committing to memory — common in school/academic contexts.