A row, column or layer will be called a line, as all rules and tips apply to any dimension.
The exponent on a number will be called a hint, as it is ingame.
Boxes that are part of the solution will be called marks or marked boxes, as you mark them during gameplay.
If there is a hint to the number in a line, the consecutive blocks seperated by the gap will be called parts.

The numbers on the sides of the blocks denote exactly how many consecutive blocks this line are valid or as I'll call them, marked, and all others should be removed. The line for this rule is the whole column/row/layer that is 90° to the number, or in other words, if the number is on top of a block, it is used for the whole column.
This number means consecutive blocks, blocks without any gaps. A 5 means there are 5 marks next to each other an no other blocks.

The exponent to a number is called a hint in-Game. It's a bit of a misnomer, as it's not a hint - numbers without hints do not have any gaps, ever. It tells you that, and how many, gaps are between the blocks. For example, a 5^2 means there are 5 blocks in this line, but two gaps in between. The hint does not tell you where or how long the gaps are. The end of the line does not count as a gap.
To illustrate, taking X as blocks and - as gaps, all those would be valid for 5²:
---X-X-XXX---
XX--XX-X--
XXX---X-----X

Most of the following tactics will be the same as normal nonogram tactics. If you already know nonograms well, you can skip most of those.

At the start, go through all layers and mark out those lines in every dimension that are as long as their whole dimension. If the puzzle is 11 blocks wide, start out by marking all columns that have an "11" on the end and so on. Do this before attempting to solve the puzzle.
Often, you save yourself plenty of time because those lines will be very helpful to other dimensions. If you don't do this, you will eventually through the normal solving process, sure, but it's very helpful to do that before you do anything else.

Unlike in normal nonograms, in Voxelgram this most often only works for unhinted numbers.
This common tactic works for all lines that are shorter than the double of the number, so if your number is 5, it will work for lines up to 9 blocks.
Let's say you have a number of 8 and a line length of 10 blocks. If you compare the furthest possible location of your marked blocks to one side (block 1-8) with the furthest possible location to the other side (blocks 3-10), the conjunction, blocks 3-8, are blocks that can be safely marked as they must be valid.

(Image courtesy of Jsimlo at the English language Wikipedia[en.wikipedia.org])
Personally I find it easiest to just subtract your number from the line length (in the example, 10-8) and leave as many boxes as that results in unmarked on each end of the line and mark the rest.

If you have a hinted number, it gets complicated, as it often does with hinted numbers.
If you have only one part left to fill, say you have a hint of 1 and one part already defined, you can just use the above for the rest of the blocks in your number.

If you have as many gaps as your hint demands and if none of the parts is large enough that you could place an additional gap in it and fit your number in leaving one of the parts of the line unused, you can actually do nearly the same as with the unhinted numbers, but you gotta do it for every part on their own. Subtract the amount of total blocks in all parts but one from your number, then use the resulting number on the part you didn't count like in the simple example above. Repeat that process for all parts.
Say you have this:

To determine the first gap, you fully fill up the second one, which gives you a "new" number to work with, 6-4=2, and use this like the above.
To Determine the second part, you use 6-3=3 as the number.

To speed that process up, you can use maths: Subtract your number from the total amount of blocks in the line, and the result is how much leeway you should leave from every edge. In this case, 7 (blocks) - 6 (number) = 1 (leeway)

This, too, only works for unhinted numbers or hinted ones where you are already sure how long a part is.
If you already have a block marked and it's less far away from the edge than its value, you can determine more blocks that have to be valid similar to the previous tactic. As there are no gaps, the furthest possible location your marks can start is where you have that one block, so you can compare it to if it started at the start of the line.

(Image courtesy of Jsimlo at the English language Wikipedia[en.wikipedia.org])

If your hint is one less than your number, you know that each part has to be just one block wide, so you can remove any blocks adjacent to any marked blocks:



Similarly, you can do the same for consecutive marked blocks that are the maximum possible size of a part, which is the hint subtracted from the number, 5-3=2 in the example:



Additional hint: If you have a part that is the maximum possible size (number - hint), every other part is exactly one block wide

This works if the line is exactly as long as your number plus your hint, counting gaps in the line as one, no matter how long they are (so two blocks, 3-block-wide gap and another two blocks would count as 5, not 7).
In this case, you know that all remaining gaps can be at most one block wide and that the existing gaps cannot be any bigger than they already are.
If the maximum part length is one (the hint being 1 smaller than the number) you can just mark every other block starting with the first one and remove the rest:


If the maximum part length is longer, you cannot determine the position of the gaps, but since you know that the existing gaps can't be any bigger, you can mark every block that is at an edge:



In case there are no existing gaps, this also works for the two ends of the line.

If you have an unhinted number and two marked blocks in the line, you can just join them together, as there can be no gaps.
You can also safely remove any blocks that are further away from any marked blocks than the number of marked blocks subtracted from your number.
Example:



If you have gaps, it gets a bit more complicated.
This only works if you have as many or more marked blocks in the line already as there are parts and you can determine as many parts as in the hint demands (which is simply hint+1), meaning that at least that many marked blocks are as far away from the next marked block that they can't be in the same part.
Calculating that distance is not hard:
Determine the largest number of consecutive marked blocks you could have, which you get by subtracting the hint from the number. Two blocks that are guaranteed not to be in the same part have one less than that many blocks in between them.

Once you verified that you can determine all the parts, you can safely join all blocks that are in the same part. This only works if you can determine all the parts, not just some.
Similarly, you can remove all blocks that are further than the number subtracted by the marked blocks away from any of your blocks.
Example:

You know that the largest part can be 6-1=5 blocks long at most, so the first two marked blocks have to be in their own part. As you only have two parts, you know that the last two have to share one, so you can join them:

After that, you can remove all blocks that are your number minus the marked blocks, so in this case 6-4=2, away from any of the marked blocks.

Those are small things that I noticed but don't deserve their own section.
At the time, two small things, I may add to this later.

Always be on the lookout for parts that have to be marked to fit the number in without needing more gaps than the hint tells you to. It's quite obvious, really, but very easily overlooked while deep into solving other stuff. A simple example:

Obviously the two blocks on the right have to me marked, or you'd have two gaps instead of one.

Always make sure to clean up. If you have more parts than your number demands but already have marked blocks in as many parts as your number demands, just remove all other parts as they can't be marked without introducing more gaps than you should have. Example:


A block that has no number on it from any direction (blank on top, side and front) will always be marked. But as those blocks also have no chance of helping you in the solution, that is just a nice-to-know.