A 3D-printer produces a cube with a volume of 300 cubic centimeters (cm³). If the printer is set to produce a second cube with side lengths doubled from the first cube. What is the volume of the second cube?

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The volume of a cube is given by the following equation, where \(s\) is the side length.

$$ V=s^3 $$

If we double the side lengths, we are effectively changing \(s\) into \(2s\).

$$ V=(2s)^3 $$ $$ V=8s^3 $$

The value of \(V\) is 8 times larger than in the initial equation. Since the volume of the first cube was \(300\text{ cm}^3\), the volume of the new cube will be:

$$ 8 \cdot 300\text{ cm}^3 $$ $$ = \boxed{2400\text{ cm}^3} $$

We can solve for the side of the first cube.

$$ V_1=s_1^3 $$ $$ 300 = s_1^3 $$ $$ s_1=\sqrt[3]{300} $$

Doubling this side and finding the volume of the second cube:

$$ s_2=2\cdot \sqrt[3]{300} $$ $$ s_2=2\sqrt[3]{300} $$ $$ V_2 = s_2^3 $$ $$ V_2= (2\sqrt[3]{300})^3 $$ $$ V_2=2^3\cdot 300 $$ $$ V_2=\boxed{2400} $$