To evaluate the expression \( c^2(8 - b + a^3) + 7 \cdot a \) with the values \( a = 2 \), \( b = 4 \), and \( c = 3 \), we can substitute these values step by step.
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Calculate \( a^3 \): \[ a^3 = 2^3 = 8 \]
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Substitute the values of \( a \) and \( b \) into \( 8 - b + a^3 \): \[ 8 - b + a^3 = 8 - 4 + 8 = 12 \]
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Calculate \( c^2 \): \[ c^2 = 3^2 = 9 \]
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Now substitute into the expression \( c^2(8 - b + a^3) + 7 \cdot a \): \[ c^2(8 - b + a^3) = 9 \cdot 12 = 108 \]
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Calculate \( 7 \cdot a \): \[ 7 \cdot a = 7 \cdot 2 = 14 \]
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Finally, add the two parts: \[ 108 + 14 = 122 \]
Therefore, the value of the expression is \( \boxed{122} \).