The problem asks us to expand the expression $(3m^3 + 1)^2$.

1. Problem Description

The problem asks us to expand the expression $(3m^3 + 1)^2$.

2. Solution Steps

To expand $(3m^3 + 1)^2$, we can use the formula for the square of a binomial:

$(a + b)^2 = a^2 + 2ab + b^2$.

In our case, $a = 3m^3$ and $b = 1$. Therefore,

$(3m^3 + 1)^2 = (3m^3)^2 + 2(3m^3)(1) + (1)^2$

$= 9m^6 + 6m^3 + 1$.

3. Final Answer

$9m^6 + 6m^3 + 1$