1. **Problem statement:** Given the equation $$\frac{y}{p^2} + \frac{1}{p^2} = 7,$$ calculate the value of $$p^2 + \frac{1}{p^3}.$$ 2. **Rewrite the given equation:** Combine the terms on the left-hand side since they have the same denominator: $$\frac{y + 1}{p^2} = 7.$$ 3. **Isolate the numerator:** Multiply both sides by $$p^2$$ to get $$y + 1 = 7p^2.$$ 4. **Express $$y$$ in terms of $$p^2$$:** $$y = 7p^2 - 1.$$ 5. **Calculate the value of $$p^2 + \frac{1}{p^3}$$:** We need to find $$p^2 + \frac{1}{p^3}$$ but we do not have enough information about $$p$$ or $$y$$ to directly calculate this value. The problem as stated is incomplete or missing additional information to solve for $$p^2 + \frac{1}{p^3}$$. **Conclusion:** Without additional information or constraints, the value of $$p^2 + \frac{1}{p^3}$$ cannot be determined from the given equation. --- **Note:** The user asked for questions from 26 e to 31 but only the first question is solved as per instructions. The total number of distinct questions in the message is 31.