The simple way is don’t test Object vs Object collisions, populate an array with the center point of each ball. Then, from each center scan a a square of size 4*radius centered on that point (you can optimize this a bit by not using a square, at the expense of making the code more complex). If there’s another center in this square, only then do you check to see if they’re within 2*radius of each other (and therefore colliding). You can further optimize this by reducing the resolution, and rounding the ball position, reducing the number of checks you need to do.
Another way, is to divide your space into a grid, and store the objects in grid regions. You only need to check for collisions between objects in adjacent grids.