SU free doesn’t offer the solid tools that would allow you to do that subtraction of the sphere from the base in one quick operation.
However, it allows you to do faces intersections.
Use this procedure:
1 - Once the sphere is positioned on the base, as shown by your image, move a copy of the sphere aside to preserve it;
2 - Select the sphere and the base;
3 - Right click on the selection to bring up a contextual menu;
4 - In this menu, choose Intersect faces → With model. The sphere shall crease a circle on top of the base as well as a recessed concave part of a sphire. You will see that as you follow the following steps;
5 - Delete the sphere and then delete the above mentioned circle. That shall reveal a bowl shaped in the base;
6 - Select the base and create a group. This will allow you to manipulate the base independently from the sphere, if you require it;
7 - Move the copy of the sphere back to fit on the modified base.
A slightly different approach. This presumes the sphere is already a component or group and eliminates the need to move a copy away and later back into place.