The 8th Amendment is not typically seen as an amendment that has anything to do with the right to privacy. The right to privacy is not actually explicitly laid out in the Constitution. Instead, justices have argued that the right is implied by various of the amendments to the Constitution. The rights guaranteed by those amendments imply that there is a more general right to privacy. The 8th Amendment is not one of those amendments.
The 8th Amendment protects people against excessive bail, excessive fines, and “cruel and unusual” punishments. None of these things really has anything to do with privacy. Instead, they have to do with protecting people who have already been convicted of crimes from being punished in excessive ways. The right to privacy is much more connected to amendments like the 4th Amendment that protect people from intrusions into their lives by the government. The 8th Amendment, by contrast, only comes into play when a person has already been convicted of a crime. Therefore, it is not connected to the right to privacy.