Step 1: Identify the structure.
The given molecule is a substituted cubane derivativeIt contains methyl groups and ring hydrogens attached to the cubane framework
Step 2: Identify different proton environments.
There are two main types of protons present in the molecule: protons of the methyl groups and protons directly attached to the cubane ring carbons
Step 3: Check equivalence of methyl protons.
Due to symmetry in the molecule, all methyl groups are chemically equivalentTherefore, all methyl protons give one type of signal
Step 4: Check equivalence of ring hydrogens.
The hydrogens attached directly to the cubane skeleton are also related by symmetryHence, they are chemically equivalent to each other
Step 5: Count chemically non-equivalent proton types.
One type corresponds to methyl protons and one type corresponds to cubane ring protons
Step 6: Conclusion.
Thus, total number of chemically non-equivalent proton types is
\[
\boxed{2}
\]