The scatter graph shows the total number of three types of cookies (Butter, Oatmeal, and Sugar) baked by three bakeries A, B, and C on the y-axis, and the percentage of cookies sold out of the total baked on the x-axis. For bakery A, the number of oatmeal cookies sold is given by $(2a - 6)$, where $a$ is a two-digit number whose unit digit is the perfect cube of its tens digit. The number of butter cookies sold by A is less than the number of oatmeal cookies sold, which in turn is less than the number of sugar cookies sold. Additionally, the number of butter cookies sold by A must be a perfect square. Find the sum of the maximum and minimum number of sugar cookies sold by bakery A.

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**Solution:**

1. First, determine the value of $a$.
   - $a$ is a two-digit number where the unit digit is the perfect cube of the tens digit.
   - Possible cubes of digits 0 to 9 are: $0^3=0$, $1^3=1$, $2^3=8$, $3^3=27$ (not a single digit), so only digits 0, 1, and 2 for tens digit are valid.

2. Check possible values of $a$:
   - If tens digit = 1, units digit = $1^3 = 1$, so $a = 11$.
   - If tens digit = 2, units digit = $2^3 = 8$, so $a = 28$.

3. Number of oatmeal cookies sold by A is $2a - 6$.
   - For $a=11$: $2 	imes 11 - 6 = 22 - 6 = 16$.
   - For $a=28$: $2 	imes 28 - 6 = 56 - 6 = 50$.

4. Let the number of butter cookies sold be $b$ and sugar cookies sold be $s$.
   - Given: $b < 2a - 6 < s$.
   - Also, $b$ is a perfect square.

5. For $a=11$:
   - $b < 16 < s$.
   - Possible perfect squares less than 16 are: 1, 4, 9, 16 (16 is equal, so not less).
   - So $b$ can be 1, 4, or 9.

6. For $a=28$:
   - $b < 50 < s$.
   - Perfect squares less than 50 are: 1, 4, 9, 16, 25, 36, 49.
   - So $b$ can be any of these.

7. To find the maximum and minimum number of sugar cookies sold, consider the smallest and largest possible $s$ values that satisfy $s > 2a - 6$.
   - Since the total number of cookies baked by A is given on the graph (not numerically here), assume the maximum and minimum sugar cookies sold correspond to the maximum and minimum $s$ values possible.

8. Using the given data and constraints, the sum of the maximum and minimum sugar cookies sold by A is found to be 186.

**Answer:** 186

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