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sqdancefan
Again, a spreadsheet or suitable calculator makes this short work.

The sum is 184.

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The terms being summed are ...
  2·3² +3 = 2·9 +3 = 18 +3 = 21
  2·4² +3 = 35
  2·5² +3 = 53
  2·6² +3 = 75
Their total is
  21 +35 +53 +75 = 184
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