Okay so keep the claim ditch the explanation.
To construct that explicit proof could I draw a picture like that one you posted in the link with picture of the two forks that divide the grid up?
Yes. Usually a picture shows just one example (e.g., a board of specific dimensions) and may not be as general as a real proof, but it may go a long way in conveying the idea. I am not sure you need the forks. That picture deals with a more difficult problem where the two removed squares can be anywhere. In your case they are in the corners.
Alright just #2 remains now
#2 This kind of reminds me of series and sequences from calc 2, not sure what it asking. Is it asking me to find what the soultions would be for any given n?
a. 1 = 1; 1 + 3 = 4; 1 + 3 + 5 = 9; 1 + 3 + 5 + 7 = 16;
b. 1 + 3 + ... + (2n + 1) = ???
c. 1 = 1; 1 + 8 = 9; 1 + 8 + 27 = 36; 1 + 8 + 27 + 64 = 100;
d. 1 + 8 + ... + n^3 = ???