Number 1

• The first statement is $\color{#D61F06} \text{false}$ . A prime number is always greater than 1.

• The second statement is $\color{#D61F06} \text{false}$ .

• The third statement is $\color{#20A900} \text{true}.$ 6 is the smallest perfect number.

• The fourth statement is $\color{#20A900} \text{true}$ . Since 0 isn't positive, $0^3 + 1^3 = 1$ is invalid in this case.

There are $\color{#D61F06} \boxed{2}$ false statements.