Regional problem · Combinatorics

A number is written in every cell of an \(8 \times 8\) table. A move consists of choosing any \(3 \times 3\) square of the table (nine cells) or any \(4 \times 4\) square (sixteen cells) and increasing by \(1\) each of the numbers standing in the chosen square.

Is it true that every starting table can be turned, by a sequence of such moves, into a table in which all the numbers are even?

One admissible \(3 \times 3\) square and one admissible \(4 \times 4\) square. Squares may be chosen anywhere inside the board and may overlap.