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\[ \sum_{i=3}^{6} (8i^2 + i) = (8(3)^2 + 3) + (8(4)^2 + 4) + (8(5)^2 + 5) + (8(6)^2 + 6) \]
\[ = (72 + 3) + (128 + 4) + (200 + 5) + (288 + 6) \]
\[ = 75 + 132 + 205 + 294 \]
\[ = 606 + 294 \]
\[ = 900 \]
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