1. int Colors() {
2.   return int(random(0, 255));
3. }
4. color c = color (Colors(), Colors(), Colors());
5. color c2 = color (Colors(), Colors(), Colors());
6. color[][] grid = new color[10][10];
7. void setup() {
8.   size(500, 500);
9.   rectMode(CENTER);
10.   for (int i = 0; i < 9; i++)
11.     for (int j = 0; j < 9; j++)   
12.       grid[i][j]=255; //white
13. }
14. void draw()
15. {
16.   background(c2);
17.   Board();
18.   //get mouse position less border width
19.   int mX=(mouseX-25);
20.   int mY=(mouseY-25);
21.  
22.   //map to range 0 to 9
23.   mX=mX/50;
24.   mY=mY/50;
25.   //if in range set colour in array
26.   if (mX>=0 && mX<10)
27.     if (mY>=0 && mY<10)
28.       grid[mX][mY]=c;
29.      
30.  
31. }
32. void Board()
33. {
34.   for (int i = 0; i < 9; i++)
35.     for (int j = 0; j < 9; j++) {
36.       if (grid[i][j]==c)
37.         fill(c);
38.       else
39.         fill(255);     
40.       rect(50+i*50, 50+j*50, 50, 50);
41.     }
42. }

...is one way  (I hacked out some of the unused bits of your code for brevity and turned the cursor back on to help see whats going on).