They look like teeny green tomatos, and have milky-white stuff inside. There are clusters of it from deep inside the soil up to the top. This is a houseplant during the winter, but outside from spring thru fall. I noticed this at the same time as lots of white specks on the leaves (aphids?), and wondered if they were a related problem - or not a problem at all. . . . .
What Are the Tiny Pale Green “Balls” in My Cyclamen’s Soil?
Certified GKH Gardening Expert
The green balls are root nodules and are perfectly normal for a cyclamen. It is how they store energy.
The white specks could be aphids or one of a few other similar pests. They are all treated the same way with a standard pesticide. I personally like neem oil. It is organic, safe for people and pets and "good" bugs and very effective. Here is more information: