1. The problem asks to evaluate the squares of the expressions $(5 + 1)$ and $(7 - 5)$.\n\n2. Recall the formula for squaring a number: $a^2 = a \times a$.\n\n3. First, calculate $(5 + 1)^2$.\n\nCalculate inside the parentheses: $5 + 1 = 6$.\n\nThen square the result: $$6^2 = 6 \times 6 = 36.$$\n\n4. Next, calculate $(7 - 5)^2$.\n\nCalculate inside the parentheses: $7 - 5 = 2$.\n\nThen square the result: $$2^2 = 2 \times 2 = 4.$$\n\n5. Final answers: $(5 + 1)^2 = 36$ and $(7 - 5)^2 = 4$.