Step 1: Define Variables. Let $AB$ be the building of height $7 \text{ m}$ and $CD$ be the cable tower. Let the distance between the building and the tower be $x \text{ m}$.

Step 2: Calculate Distance. In $\Delta ABD$, the angle of depression to the foot of the tower is $45^\circ$. Using $\tan 45^\circ = 1$, we write $\tan 45^\circ = \frac{AB}{BD} \Rightarrow 1 = \frac{7}{x}$. Solving for $x$, we get $x = 7 \text{ m}$.

Step 3: Calculate Height Difference. Draw a perpendicular from $A$ to $CD$ meeting at $E$. In $\Delta ACE$, the angle of elevation is $60^\circ$. Using $\tan 60^\circ = \sqrt{3}$, we write $\tan 60^\circ = \frac{CE}{AE} \Rightarrow \sqrt{3} = \frac{CE}{7}$. Solving for $CE$, we get $CE = 7\sqrt{3} \text{ m}$.

Step 4: Calculate Total Height. The total height of the tower is $CD = CE + ED$. Since $ED = AB = 7 \text{ m}$, we have $CD = 7\sqrt{3} + 7 = 7(\sqrt{3} + 1) \text{ m}$.