As I've created my tower and added floors, I've collected data on the items needed to complete each floor. The requirements for the floors do follow a pattern, and so, even though I have not completed my tower fully, I have projected the ingredients out for all the floors.
Note that if I have done my math wrong, or the actual system has some kind of leap in the ingredients somewhere that I could not have predicted with my data, then this could be inaccurate.
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The original project for a Tower, before you can enter, which also gives you your Floor 1, Storey 2 costs 20 Urth Blocks, 1 General Building Permit, 200 Snails, 20 Breaking Ground (Shovel) Work Units, 4 Girders, 16 Wall Segments, 20 Construction (Construction Tool) Work Units.
Floor Ingredients
Floor 2, Storey 3: 8 Wall Segments, 40 Urth Blocks, 8 Girder, 24 Snails, 25 Construction (Construction Tool) Work Units, 4 Beams, 8 Metal Bars, 53 String, 1 General Building Permit, 25 Elevation (Tinkertool) Work Units
Floor 3, Storey 4: 8 Wall Segments, 60 Urth Blocks, 12 Girders, 24 Snails, 30 Construction (Construction Tool) Work Units, 6 Beams, 12 Metal Bars, 106 String, 1 General Building Permit, 30 Elevation (Tinkertool) Work Units
Floor 4, Storey 5: 8 Wall Segments, 80 Urth Blocks, 16 Girders, 24 Snails, 35 Construction (Construction Tool) Work Units, 8 Beams, 16 Metal Bars, 159 String, 1 General Building Permit, 35 Elevation (Tinkertool) Work Units
Floor 5, Storey 6: 8 Wall Segments, 100 Urth Blocks, 20 Girders, 24 Snails, 40 Construction (Construction Tool) Work Units, 10 Beams, 20 Metal Bars, 212 String, 1 General Building Permit, 40 Elevation (Tinkertool) Work Units
Floor 6, Storey 7: 8 Wall Segments, 120 Urth Blocks, 24 Girders, 24 Snails, 45 Construction (Construction Tool) Work Units, 12 Beams, 24 Metal Bars, 265 String, 1 General Building Permit, 45 Elevation (Tinkertool) Work Units
Floor 7, Storey 8: 8 Wall Segments, 140 Urth Blocks, 28 Girders, 24 Snails, 50 Construction (Construction Tool) Work Units, 14 Beams, 28 Metal Bars, 318 String, 1 General Building Permit, 50 Elevation (Tinkertool) Work Units
Floor 8, Storey 9: 8 Wall Segments, 160 Urth Blocks, 32 Girders, 24 Snails, 55 Construction (Construction Tool) Work Units, 16 Beams, 32 Metal Bars, 371 String, 1 General Building Permit, 55 Elevation (Tinkertool) Work Units
(I'm assuming that when they say 9 floors, they mean nine stories, not the number on the elevator menu.)
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Not including the original base of the Tower, Wall Segments, Snails, and General Building Permits stay a constant of 8, 24, and 1, respectively. Urth Blocks start at 40, and increase by 20 each time. Girders and Metal Bars start at 8, and increase by 4 each time. Construction Work Units and Elevation Work Units start at 25, and increase by 5 each time. Beams start at 4, and increase by 2 each time. String starts at 53, and increases by 53 each time.
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TOTAL (Floors Only) --- Boring Math Breakdown
This totals out to 56 Wall Segments, 700 Urth Blocks, 140 Girders, 168 Snails, 280 Construction Work Units, 70 Beams, 140 Metal Bars, 1484 String, 7 General Building Permits, and 280 Elevation Work Units.
Which equals 56 Beams, 224 Wood Posts, 672 Boards, 840 Barnacle Talc, 3500 Lumps of Earth, 1400 Lumps of Loam, 700 Heavy Gas, 1120 Molybdenum Ingots, 1680 Plain Metal Ingots, approximately 21 Metal Rods (168 / 8 = 21) plus at least 3 fully rocked out sloths, loads of energy, 280 Wood Posts, 280 Copper Ingots, 420 Tin Ingots, 7420 Thread, 3500 Currants (7 * 500 Currants = 3500 Currants) plus 7 dramatic entrances to the Bureaucratic Hall and 70 whole seconds of waiting, and loads of energy.
Which happens to equal 720 Wood Posts, 672 Boards, 840 Mortar Barnacles, 3500 Lumps of Earth, 1400 Lumps of Loam, 4200 General Vapor, 2800 Plain Metal Ingots, 5600 Blue Elements, 56000 Sparkly Elements, approximately 21 Metal Rods, 700 Plain Metal Ingots, 8400 Green Elements, 16800 Red Elements, 3360 Red Elements, 3360 Blue Elements, 3360 Green Elements, 51940 Fiber, 3500 Currants.
Which just happens to equal 3552 Boards, 840 Mortal Barnacles, 3500 Lumps of Earth, 1400 Lumps of Loam, 4200 General Vapor, approximately 21 Metal Rods, 3500 Plain Metal Ingots, 20160 Red Elements, 8960 Blue Elements, 11760 Green Elements, 56000 Sparkly Elements, 51940 Fiber, and 3500 Currants.
Which finally equals 14208 Planks, 840 Mortal Barnacles, 3500 Lumps of Earth, 1400 Lumps of Loam, 4200 General Vapor, approximately 21 Metal Rods, 17500 Chunks of Metal, 20160 Red Elements, 8960 Blue Elements, 11760 Green Elements, 56000 Sparkly Elements, 51940 Fiber, and 3500 Currants.
TO RECAP, TO FINISH ALL YOUR FLOORS (not including initial tower cost, which is above but was too lazy to break down that) YOU WILL NEED...
14208 Planks
840 Mortal Barnacles
3500 Lumps of Earth
1400 Lumps of Loam
4200 General Vapor
approximately 21 Metal Rods (21 Plain Metal Ingots + 21 Tin Ingots; not covered by this list)
17500 Chunks of Metal
20160 Red Elements
8960 Blue Elements
11760 Green Elements
56000 Sparkly Elements
51940 Fiber
3500 Currants
and loads of energy and respective tools.