You should see a standard chessboard - it is printed on paper. How many ways can you cut it up (around the squares) such that each piece has twice as many squares of one colour than of the other colour?
A piece that has $k$ squares of one color and $2k$ squares of the other color has $3k$ squares. It is a multiple of $3$. You cannot split $64$ squares in any number of parts that all have multiples of $3$ squares.