To solve the given expression \((5+1)^{2} \cdot 3\), follow these steps:
First, we evaluate the expression inside the parentheses: \[ 5 + 1 = 6 \]
Next, we raise the result to the power of 2: \[ 6^2 = 36 \]
Finally, we multiply the squared result by 3: \[ 36 \cdot 3 = 108 \]
\(\boxed{108}\)
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