1. **Stating the problem:** We need to find the sum of the series $360 - 357 + 354 - 351 + \cdots + 300 - 297$. 2. **Understanding the series:** The series alternates between addition and subtraction of terms decreasing by 3 each time, starting from 360 and ending at 297. 3. **Number of terms:** The terms go from 360 down to 297 in steps of 3. The number of terms $n$ is given by: $$n = \frac{360 - 297}{3} + 1 = \frac{63}{3} + 1 = 21 + 1 = 22$$ 4. **Grouping terms:** The series can be grouped in pairs: $$(360 - 357) + (354 - 351) + \cdots + (300 - 297)$$ Each pair has two terms. 5. **Number of pairs:** Since there are 22 terms, the number of pairs is $\frac{22}{2} = 11$. 6. **Sum of each pair:** Each pair is: $$ (a) - (a-3) = 3 $$ For example, $360 - 357 = 3$, $354 - 351 = 3$, etc. 7. **Sum of the series:** Since each of the 11 pairs sums to 3, the total sum is: $$11 \times 3 = 33$$ **Final answer:** $$\boxed{33}$$