<Question>
What is the total surface area, in square inches, of a cube with a volume of $1$ cubic foot?
</Question>

<think>
<Plan_1>
Okay, let's see. The problem is asking for the total surface area of a cube in square inches when the volume is given as 1 cubic foot. Hmm, first, I need to remember the formulas related to cubes. 

So, a cube has all sides equal, right? The volume of a cube is calculated by side length cubed. The formula is V = s³, where s is the length of a side. Then, the surface area of a cube is 6 times the area of one face because a cube has six faces, each with the same area. The formula for surface area (SA) is SA = 6s².

But wait, the problem gives the volume in cubic feet, and the answer needs to be in square inches. I need to convert units here. Let me start by finding the side length in feet since the volume is given in feet.
Since the volume is 1 cubic foot, that means s³ = 1 ft³. So, solving for s, we take the cube root of 1 ft³, which is 1 foot. So each side of the cube is 1 foot long.

But now, I need to convert the side length from feet to inches because the surface area needs to be in square inches. There are 12 inches in a foot, so 1 foot is 12 inches. Therefore, each side of the cube is 12 inches long.

Now, calculate the surface area. Using the formula SA = 6s². Plugging in s = 12 inches, we get SA = 6 * (12)².
Let me compute that. 12 squared is 144, so 6 * 144. Let me do 100*6=600, 40*6=240, 4*6=24. Adding those together: 600 + 240 is 840, plus 24 is 864.

Wait, that seems right. Let me double-check.

<prompt_1.1> Verify the surface area calculation step by step. </prompt_1.1>

But just to make sure I didn't skip any steps. The volume is 1 cubic foot, which is 1 ft³.
Since all sides are equal in a cube, each side is 1 foot. Convert that to inches: 12 inches. Then surface area is 6 times one face's area. Each face is 12x12, which is 144 square inches. Multiply by 6: 144*6=864.
</Plan_1>

<Execution_1>
<execution_1.1>
12 inches is 1 foot. So side length is 12 inches. Area of one face is 12*12=144. Total surface area is 6*144. 144*6: 100*6=600, 40*6=240, 4*6=24. 600+240=840, 840+24=864.
</execution_1.1>
</Execution_1>

<Final_answer>
Therefore, the total surface area of the cube is $\boxed{864}$ square inches.
</Final_answer>
</think>