First of all, you need to understand 120V/single breaker vs. 240V/double breaker. The current is set for each wire. So a 60A double-breaker gets 60A on each wire, for a total of 60A @ 240V or (theoretically, if all balanced) 120A @ 120V. It doesn't let you use "30A wire" and double it to 60A. There seems to be a lot of confusion about this from people who don't understand how the US 240V/120V system works. Almost everything larger than 20A will be a double-breaker, 4 wire (hot, hot, usually but not always neutral, ground) circuit. When we refer to a "30A circuit", that is immediately understood to mean "30A @ 240V, 2 hot". If a circuit is only 240V (water heater) then neutral is not needed. If a circuit is 240V/120V (clothes dryer) then it needs a neutral.
Next we get to wire size. Wire size generally varies based on:
- Type of wire/cable - wire in conduit can often carry more current than wires inside NM cable (a.k.a., Romex)
- Copper vs. aluminum - Aluminum typically needs to be one size larger to carry the same current as copper. In addition, aluminum is (for historical reasons) not usually used for 15A or 20A circuits but is very common for larger circuits and especially for feeders (utility to main panel, main panel to sub panels).
- Temperature rating - The minimum is usually 60 C, higher allowed for 75 C (which generally is allowed for breakers (so panel to panel) and some other devices and for 90 C (much less common).
- Continuous use derate - For continuous use (there are formal definitions - but this includes things like water heaters, EV charging, HVAC), you only get to use 80% of the wire/breaker rating - e.g., if you need to actually use 40A then you have to use 50A rated wire and breaker. But people confuse this sometimes (and there are some exceptions...) to think if they have a 40A actual continuous load needs only 40A wire but a 50A breaker (wrong, and doesn't scale to 60A anyway).
- While breakers are supposed to, usually, be equal to or smaller than the wire size, there is an exception for rounding - e.g., if you have 55A rated 6 AWG NM copper then you can use a 60A breaker because 55A breakers are not available. (but that doesn't apply for 8 AWG aluminum rated for 40A)
Charts are available, such as this one that list allowable current.
8 AWG aluminum gets 40A at 75 C, and 45A at 90 C. Unlikely the terminations are rated for 90 C - even if that was the case the rounding would only get you to 50A. So no matter how you slice it, this is no good.
Bottom line: Unless you replace with larger wires (6 AWG = 50A breaker, 4 AWG = 65A breaker - not available so use 70A breaker, 2 AWG = 90A breaker), you are limited to (a) a 40A breaker and (b) continuous loads should be a maximum of 32A (40 x .8).
Note that the sub panel (in the garage) can have a main breaker that is larger than 40A - even 200A would be fine because it functions just as a shut off switch/disconnect and not to protect the feed wires.