You cannot upcast spells from the Staff of Power outside of those it "forces" you to upcast (such as 5th-level fireball)
The description of the Staff of Power (DMG, p. 202) explicitly describes what level its spells are cast at, and gives a single number for how many charges it costs:
Spells. While holding the staff, you can use an action to expend 1 or more of its charges to cast one of the following spells from it, using your spell save DC and spell attack bonus: cone of cold (5 charges), fireball (5th-level version, 5 charges), ...
I won't include the rest of the spells, cone of cold and fireball serve as sufficient examples; cone of cold would be cast at its base level1, and fireball would be upcast at the level it specifies (5th-level).
No further text seems to imply that the level that these spells are cast at can be in any way modified by using a different number of charges (not only upcasting, say, cone of cold or fireball to 6th-level or higher, but also there's no way to cast fireball at 3rd- or 4th-level by using fewer charges, for example).
As a counterexample, consider the description of wands; let's take the Wand of Fireballs as our example (DMG, p. 210):
The wand has 7 charges. While holding it, you can use an action to expend 1 or more charges to cast the fireball spell (save DC 15) from it. For 1 charge, you cast the 3rd-level version of the spell. You can increase the spell slot level by one for each additional charge you expend.
Since the Staff of Power does not describe that you can upcast using additional charges, whereas the Wand of Fireball does, then by omission, we must conclude that the Staff of Power cannot do this.
1 We know that spells cast from magic items are cast at their base level unless specified otherwise because of the generic information on spells cast from magic items from DMG, p. 141 (under the heading "Spells"):
Some magic items allow the user to cast a spell from that item. The spell is cast at the lowest possible spell level, doesn't expend any of the user's spell slots, and requires no components, unless the item's description says otherwise.