As you refer to the molar absorption coefficient or molar absorptivity (ε) as it is also known, the word molar (mol/L) conditions the units that should be used. The units of ε are L/(cm x mol) usually but an equivalent presentation is mL/(cm x mmol). In the latter case the unit mL can be replaced by cubic centimeters: cm3/(cm x mmol). Then the expression derives in
cm2/mmol.
It could not be cm2/mol because it would not be molar absorptivity, in any case, this version can be called absorptivity simply, that is, without the word molar.
Nor can it be m2/mol. Why? 1 m is equivalent to 100 cm and 1 mol equals 1000 mmol, if it is replaced in m2/mol it is obtained that:
m2/mol = (100 cm)2/1000 mmol
m2 /mol = 10000 cm2/1000 mmol
m2/mol = 10 cm2/mmol
In conclusion, cm2/mol y m2/mol are units of absorptivity or absorption coefficient but not specific units of molar absorptivity.