To determine the value of $X_8$, I need to know the exact algorithm or pattern used to calculate these values. The values you provided for $X_1, X_2, X_3, \dots, X_7$ might follow a specific mathematical or numerical relationship, such as a sequence or a set of operations (addition, multiplication, or a more complex rule).

Could you please specify the algorithm or give any clues about how these values are calculated? Once I have that, I can proceed with calculating $X_8$.