'a piece of information' is just one fact, or one paragraph, or one document, depending on how much information you measure in 'a piece'. 'some pieces of information' is the plural of 'a piece of information', so it is an indefinite number of pieces of information. 'some information' is completely indefinite about number because it envisions 'information' as uncountable.
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Nakamura Yo What would be the difference among 'some information', 'a piece of information', and 'some pieces of information'? Thank you.Note that it's always 'difference between', not 'difference among'.