Answer: I can't tell without looking at the fruit just what the problem might be. I suspect either poor pollination or a problem called blossom end rot.
Most squashes and cucumbers have separate male and female flowers on the same plant. So, to produce fruit, pollen from male flowers must be transferred to the female flowers. The female blossoms have what looks like a tiny squash or cucumber behind the flower. The tiny fruit is the ovary, full of eggs not yet fertilized via pollen from male flowers. Male blossoms have long-stalked stamens, each with pollen-filled anthers. Visiting bees and other types of insects provide the transfer of pollen from the male to the female blossoms. Don't worry if the earliest blooms on squash or cucumber plants fall off before they set any fruit. The male flowers of cucumbers and squash often bloom and wither before the female blossoms start appearing. So be patient with squash and cucumber plants. Eventually, most will produce both male and female flowers. Once blossoms of both sexes are opening at the same time, and if there is still no fruit formation, there may be poor pollination.
Blossom end rot is a physiological condition caused by a lack of calcium at the growing tip of the fruit. While your soil may have adequate calcium, fluctuations in soil moisture content from dry to wet really increase the incidence of blossom end rot. The damage occurs as cells die at the tip of the fruit. In time (and as the fruit grows) the spots enlarge and turn black. So, by the time you see it, the damage actually has already occurred some time back. Remedies include: having a soil test to make sure calcium levels are adequate, adding organic matter to a sandy soil to increase its moisture holding capacity, keeping plants evenly moist, especially during the development of the first fruits (mulch helps maintain soil moisture), and spraying plants with a Blossom End Rot spray (contains calcium) which can usually be purchased from your local garden center.
I hope this information helps you determine just what the problem might be. Best wishes with your zucchini.
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