This is essentially correct.
There is no such thing as a "standard door" but the closest you can get in North America 30"x80in". Interior doors are 1.375" thick while Exterior doors are 1.75" thick. Again, there are lots of different doors but this is what we can call the standard.
This means an interior door's volume is 30 x 80 x 1.375 = 3,300 sq. In.
Your portion would be 3,300 / 365 = 9.041 sq. in. per day.
A rubik's cube is 3 inches per side, so a door is actually 14.965 sq in, larger by volume then 365 rubik's cubes. However, the door likely has cutouts for hinges and knobs. A standard bore hole has a diameter of 2.125" so you can subtract about 5 sq. in from the volume plus another 3 sq in. assuming a 4"x2" hinge cut 1/8" deep for three hinges. This leaves you with a difference of only 7 sq. in. which would likely be lost due to saw blade width during portioning.
So really, a Rubik's cube a day is just about dead on.
Next you have to worry about density. Wood varies greatly in hardness. To save some math, we will assume a standard moisture content and round to half a board foot per portion. Finally to make it a little more palatable, we will assume like many in the comments that the door will be ground up into a powder. A standard dose of Metamucil (a natural source of fiber from ground psyllium husk) is .119 oz mixed with 8 oz. of water. So we will compare the doses per common wood species.
Red Oak - 32 oz. per serving - 269 doses per day. Douglas Fir - 24 oz. per serving - 201 doses per day. Eastern White Pine - 22 oz. per serving - 185 doses per day.
Psyllium husk isn't the best example, however, because it swells greatly in liquid which makes it effective. Even then, if you quadruple the wood powder per dose you still are having more then 40 doses per day.
We can also compare it to protein powder. A standard dose scoop is just about a single ounce. This seems more doable, however, only eight servings a day is recommended by very active body builders.
If you combine the texture and volume of the protein shakes and the medicinal effects of the psyllium husks I think you would find that eating a door is likely not a healthy challenge.