Concept:
Calcium carbide ($CaC_2$) is an ionic compound consisting of $Ca^{2+}$ cations and $C_2^{2-}$ anions. The question focuses on the bonding specifically *within* the $C_2^{2-}$ dicarbide ion.
Step 1: {Analyze the structure of the $C_2^{2-}$ ion.}
The dicarbide ion ($[C \equiv C]^{2-}$) is isoelectronic with the Nitrogen molecule ($N_2$). To satisfy the octet and the formal charge, the two carbon atoms must be connected by a triple bond.
Step 2: {Identify the types of bonds in a triple bond.}
In a triple bond between two atoms, the first bond formed is a sigma ($\sigma$) bond (head-on overlap). The remaining two bonds are pi ($\pi$) bonds (lateral overlap of p-orbitals).
Step 3: {Conclude the bonding nature.}
Since the carbon atoms in $CaC_2$ are held together by a triple bond within the anion, they are specifically held by one sigma and two $\pi$ bonds.