Are there any languages which use different cases of numbers for different uses?
Yes, there are.
Finnish is one of such languages and especially interesting in that in complex numbers, all individual numerals are declined:
Matkust-i-n kolme-en maa-han. travel-IPF-1SG three-ILL country-ILL "I travelled to three countries." Hän tarvitse-e kahdeksa-a-tuhat-ta-kolme-a-kymmen-tä-kuut-ta euro-a. he/she need-3SG eight-PAR-thousand-three-PAR-ten-PAR-six-PAR euro-PAR "He/She needs eight thousand and thirty-six euro." elo+kuu-n kahde-nte-na-kymmene-nte-nä-viide-nte-nä päivä-nä life+moon-GEN two-th-ESS-ten-th-ESS-five-th-ESS day-ESS "on twenty-fifth of August"
3SG = first/third person singular
IPF = imperfect tense
ILL = illative case (for movement towards something)
PAR = partitive case (here: to be imagined as "to take some part of all euros there are")
GEN = genitive case (for posssession; here: case for the month that the specified day relates to)
ESS = essive case (for being in a state; here: case for date specification)
Many Slavonic languages have complex declension of numerals, both cardinal and ordinal ones. For example, Ukrainian:
Add lessons to your fourty- two daily tasks Додай уроки до своїх сорока двох щоденних справ add+IMP lessons+ACC to your+PL+GEN fourty+DAT two+DAT daily+PL+GEN task+PL+GEN IMP = imperative mood PL = plural GEN = Genitive case DAT = Dative case ACC = Accusative case
Note that fourty-two even declines into the different case (Dative) than the linked NP (daily tasks).
Numerals were declined in Proto-indoeuropean heavily. The declensions are preserved very well in Sanskrit and to a certain measure in Ancient Greek as well as most contemporary Slavic languages or Lithuanian.
e.g. numeral "five" in Sanskrit, Czech and Lithuanian
nom.: pañca - pět - penki gen.: pañcānām - pěti - penkių dat.: pañcabhyaḥ - pěti - penkiems etc.
Many IE languages still preserve some remains of declensions of the most basic numerals like one,two or three (e.g. in Romance languages, they still distinguish gender if not case itself).