There may be a scaling issue here. If you take a cube and:
- In edit mode, subdivide it
- In object mode, scale it along one axis
- Back in edit mode scale it back down the axis so it looks like a cube again
- And then use ShiftAltS .. 'To Sphere'
...you wind up with a similar result to yours.
In short, in object mode, CtrlA apply any scale that might be locked into the object's transform matrix.
If ever you make a non-uniform scale of something in Object Mode.. make a mental note of it, and/or keep an eye on the Transform panel in the Properties Region of the 3D view (in Object Mode). You may need to go back and bake the transform into the mesh by applying it.
If you only want a sphere shape
- Start with the cube. Ooops. Barely visible under menu.
- Edit Mode subdivide some reasonable number, perhaps 3 or 5, for vertex density and cpu efficiency
- Edit Mode To Sphere (Not Modifier). Menu Selection and Keystroke is in the image above.
Consider Shape Keys
There are always may ways to produce similar creations in Blender
Image above shows the high density cube transformed to sphere shape. Well maybe not so high density. You might start with sphere and then use shape keys to add spikes.