To find out how many times larger the volume of the saltwater tank is than the volume of the freshwater tank, we first need to calculate the volume of each tank.
The formula for the volume \( V \) of a cube with side length \( s \) is given by: \[ V = s^3 \]
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Volume of the freshwater tank:
- Side length = 15 cm \[ V_{\text{freshwater}} = 15^3 = 15 \times 15 \times 15 = 3375 \text{ cm}^3 \]
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Volume of the saltwater tank:
- Side length = 45 cm \[ V_{\text{saltwater}} = 45^3 = 45 \times 45 \times 45 = 91125 \text{ cm}^3 \]
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Calculating how many times larger the saltwater tank is than the freshwater tank: \[ \text{Ratio} = \frac{V_{\text{saltwater}}}{V_{\text{freshwater}}} = \frac{91125}{3375} \]
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Perform the division: \[ \frac{91125}{3375} = 27 \]
Thus, the volume of the saltwater tank is 27 times larger than the volume of the freshwater tank.
The answer is \( \boxed{27} \).