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$\large \sum_{k=1}^{4n} (-1)^{k (k+1)/2} \cdot k^2$

Which of the following values can the above expression take. $1) 264$ $2) 272$ $3) 280$ $4) 333$

*Details and Assumptions:- * More than one options may be correct ! Give your answer as the sum of the possible values from the given options. Give answer as 50 if you think none of the options is correct.