Diameter, d = 6 cm

The radius is half of the diameter.

$$r = \frac{d}{2} = \frac{6 \text{ cm}}{2} = 3 \text{ cm}$$

The formula for the lateral surface area of a cylinder is $LSA = 2 \pi r h$.

$$LSA = 2 \pi (3 \text{ cm})(8 \text{ cm})$$ $$LSA = 48 \pi \text{ cm}^2$$

The lateral surface area is $\boxed{48 \pi \text{ cm}^2}$.

The formula for the total surface area of a cylinder is $TSA = 2 \pi r (h + r)$.

$$TSA = 2 \pi (3 \text{ cm})(8 \text{ cm} + 3 \text{ cm})$$ $$TSA = 6 \pi \text{ cm}(11 \text{ cm})$$ $$TSA = 66 \pi \text{ cm}^2$$

The total surface area is $\boxed{66 \pi \text{ cm}^2}$.

The formula for the volume of a cylinder is $V = \pi r^2 h$.

$$V = \pi (3 \text{ cm})^2 (8 \text{ cm})$$ $$V = \pi (9 \text{ cm}^2)(8 \text{ cm})$$ $$V = 72 \pi \text{ cm}^3$$

The volume is $\boxed{72 \pi \text{ cm}^3}$.