Find the product. \( \left(7 x^{3}+1\right)\left(7 x^{3}-1\right) \) The answer is \( \square \) (Simplify your answer.)

To find the product \( \left(7 x^{3}+1\right)\left(7 x^{3}-1\right) \), we can use the difference of squares formula, which states that \( (a+b)(a-b) = a^2 - b^2 \). In this case, let \( a = 7x^3 \) and \( b = 1 \). So, we have: \[ (7x^3 + 1)(7x^3 - 1) = (7x^3)^2 - (1)^2 \] Calculating this gives: \[ (7x^3)^2 = 49x^6 \quad \text{and} \quad (1)^2 = 1 \] Thus: \[ 49x^6 - 1 \] Therefore, the answer is \( 49x^6 - 1 \).