Since any 3 points in 2D space define a circle, can any 3 points in 3D space define a sphere

Your initial statement should be that any three non co-linear points define a circle.

No, In 3D space three non co-linear points still only define a circle. this circle can be part of an infinite number of spheres with different centres and radii. You need a fourth point not on the circle of the first three to define the sphere involved.