【Analysis】The sum of length, width, and height is: $88 \div 4=22$ cm. To maximize the total lateral surface area of the cuboid, the lengths of length, width, and height must be as close as possible, i.e., $22=8+7+7$. Then, use the formula for the lateral surface area of a cuboid, which is the perimeter of the base multiplied by the height, and solve accordingly.

【Solution】The sum of length, width, and height is: $88 \div 4=22$ (cm),
To maximize the total lateral surface area of the cuboid, the lengths of length, width, and height must be as close as possible, i.e., $22=8+7+7$,
$$
\begin{aligned}
& (7+7) \times 2 \times 8 \\
= & 28 \times 8 \\
= & 224 \text { (square cm); }
\end{aligned}
$$

Answer: The maximum total lateral surface area of this cuboid is 224 square cm.
Therefore, the answer is: 224.
6. (10 points) A rectangular prism, with edge lengths all being integer centimeters, has the sum of all its edge lengths equal to 88 centimeters. What is the maximum total lateral surface area of this rectangular prism? $\qquad$ square centimeters.