Is there really no better way to write this without using a 3 on top of each beat? Is there something I could put at the top of the piece since the whole song is a shuffle like this?
Probably the same as the keyword "shuffle", but wouldn't the below example get your intention across?
Edit: Another option is to indicate the triples for the first bar, then use the word 'simile' to show the idea is to continue this for the reminder of the piece:
A directive to perform the indicated passage of a composition in a similar manner as the previous passage; similarly. One common use is to designate the continuation of the use of an articulation without repeating the articulation symbol. Often abbreviated as sim. . similarly; i.e., continue applying the preceding directive, whatever it was, to the following passageto continue to do something in the same way it was formerly notated such as pedaling or staccatos
You'll see it done in all of these ways. 12/8 is the obvious answer. Straight 8s plus a 'Shuffle' instruction is useful if you're writing into a notation program like Sibelius - but you have to make sure 'Shuffle' IS defined in the Playback Dictionary. The third way will be understood by live musicians, but will confuse computer playback.
I recommend 12/8. Using 12/8 is completely clear and unambiguous both to humans and computers.
There's also the possibiity that you're playing with a Swing feel (not precise triplets), and triplets are Cubase's best guess. If this is the case, write straight 8's and 'Swing'.
You might be able to use implicit tuplets if the groupings stay consistent throughout a significant section of the piece. Notate the first couple measures explicitly and let the musician figure it out from there (most moderately skilled musicians should be able to handle this). (Optionally, to make it more clear, you may want to add 'simile' or 'sim.' after the last explicitly marked tuple.) Again, this should only be used in long passages (preferably the entire piece) with consistent rhythmic groupings and patterns. Also, if the moderately skilled musician mentioned above can't figure it out, this probably isn't the best solution!
Here are a couple examples:
In Chopin's Fantasie Impromptu only the first sextuplet is notated and the rest are implied with slur markings, a repeated structural pattern and the fact that there are simply too many notes squeezed in. Also note that the melody (not shown) is written in non tuplets, making writing this in 12/8 impractical.
In Schubert's Impromptu Op. 90 No. 3 we are not given any tuplet notation at all. Instead, the groupings are inferred by the fact that there are 6 notes when there should clearly only be 4.
EDIT: And, of course, Moonlight Sonata, as mentioned in the OP comments. :)