Hi- there are tow main causes for the problem you describe. If some of the drupelets ("cells") are hard and white or tan in color the problem may have been white drupelet disorder caused by hot, sunny weather (even for a day or so).
The other major cause is poor pollination caused by lack of pollinators or environmental conditions like hot or cold weather, wind, etc. that damaged, or interfered with the development of, the male and female flower parts.
In either case there is little you can do to reverse or prevent these problems. Blackberry is a fairly reliable crop and these issues are usually of minor importance.