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Use quilts to create volume regions. This view is the same all 3 XYZ sides of the center cube.
Trim and merge to look like this.
TIP: mapping does not work at the "poles" as seen by [Inspect] [Mesh surface] (shows U-V lines)
replace surface as shown (revolve around another axis then trim by surfaces like view 2 then patch)
confirm with [Inspect] [Mesh surface] .
Create volume regions by quilt until this.
Section view showing internal volume lines.
Map the normal way with bricks.
Tip: use RMB pick from list when it gets busy.
A hollow sphere proceeds exactly the same except the internal spherical surface must also have its U-V lines fixed. (Center cube only for construction)
This also can produce the truncated quarter sphere. (shown with 1 element per edge)
.step files with the quilts for volume regions and "fixed" U-V.