In each generation of this family after generation i, the age at diagnosis is significantly lower than would be found in nonfamilial (sporadic) cases of this cancer (~ 63 years). what is the most likely reason?

Hereditary cases of cancer typically manifest at earlier ages than do nonfamilial/sporadic forms.

This can be explained by the two hit theory. In this theory, cancer is the result of the accumulation of mutations that occur in the DNA of a certain cell. If two mutations happen, that certain cell will be a carcinogenic cell. In hereditary cases, it's like one mutation already happen. one more and the cancer starts (that's why it's manifested earlier). In sporadic forms, the cells start with zero mutations but can suffer 2 mutations that start cancer (but takes more time).