blackberry fruit problem
I believe the problem you are seeing is called 'white drupelet syndrome'. Apache, a thornless variety developed at University of Arkansas is known to show this problem frequently and abundantly.
The exact cause of the problem is unknown. Some of have attempted to link it to a zinc deficiency, but the majority consensus is that it is a genetic flaw, manifested when developing berries are exposed to high sunlight and hot temperatures. The drupelets will show a beige, cream or whiteish coloration, never turning black as you describe. The berries are edible, and the overall taste is only slightly different.
You might try pulling shade cloth over the plants after fruit is set, but otherwise there are no recommendations for solving this problem.
Refer to your own state extension information in Kentucky for blackberry variety recommendations.