Another way to find the missing sum is to look at how much each column sum increases from the previous one, without identifying the squares directly.
List the known column sums: Column 1 = 4, Column 2 = 9, Column 3 = 16, Column 5 = 36, Column 6 = 49.
Look at the differences: \(9-4=5\), \(16-9=7\). The differences themselves increase by 2 each time (5, 7, 9, 11, 13, ...), which is the signature pattern of consecutive perfect squares. Continuing this: the next difference after 7 should be 9, so Column 4 = \(16+9=25\). The following difference should be 11, giving Column 5 = \(25+11=36\), which matches the actual value. The next difference should be 13, giving Column 6 = \(36+13=49\), which also matches, confirming Column 4 = 25 is correct.
Since Column 4's entries are 2, 10 and the unknown \(x\): \(2+10+x=25 \Rightarrow x=13\). Option C is correct. \[ \boxed{13} \]
