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 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.