I’m having trouble writing it algebraically.

Let the second of the three numbers be x. Then, the equation you want is

(x - 2)(x)(x + 2) = 1680

Find x. Brute-force isn’t a bad option here.

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1680 - can be factorized into 4x4x105 which can be sub factorized in the following way

2x2x2x2x3x5x7

Now we know the Numbers are even and consecutive so try re-arranging in steps

(2x2x3)x(2x5)(2x7) - As the numbers are even - Please arrange in this way

SO the three numbers are 10,12,14 so the sum is 36

Thank you