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I have the following MWE, but I have a problem with the alignment of the last column (under the multicolumn)

documentclassreport
usepackage[T1]fontenc
usepackage[utf8]inputenc
usepackagebooktabs
usepackagecalc
usepackagearray
usepackagecolor
%
begindocument
%
% table 1 
% evenly alined
begintable[htbp]
centering
begintabularccccc
toprule
& & multicolumn3cReduced component sizes\
%cmidrule(r)3-5 
cmidrule3-5 
% multicolumn2cInternal mode count, $m$ &10&20&30&10&20&30\
%midrule
Component & Full size & $m=4$ & $m=8$ & $m=12$\
midrule
1 & 257 & 24 & 28 & 32 \
2 & 420 & 47 & 51 & 55 \
3 & 177 & 24 & 28 & 32 \
bottomrule
endtabular
captionInformation on component level degrees of freedom
labeltab:information-overview-academic-model
endtable
% 
% table 2 
% not evenly alined
begintable[htbp]
centering
begintabularccccc
toprule
& & multicolumn3cReduced component matrix sizes textcolorredtest text added\
%cmidrule(r)3-5 
cmidrule3-5 
% multicolumn2cInternal mode count, $m$ &10&20&30&10&20&30\
%midrule
Component & Full size & $m=4$ & $m=8$ & $m=12$\
midrule
1 & 257 & 24 & 28 & 32 \
2 & 420 & 47 & 51 & 55 \
3 & 177 & 24 & 28 & 32 \
bottomrule
endtabular
captionInformation on component level degrees of freedom
labeltab:information-overview-academic-model
endtable
%
enddocument

The result I am getting is that the columns under the multicolumns are not evenly separated. And when I increase the width of the text argument to multicolumn command it becomes even worse, first example seems to be fine but with the second there is definitely a problem. Here is the output of the above code:

Any ideas are appreciated to solve this issue.
Many thanks in advance.

I suggest two kinds of solutions.

The first one with makecell which puts the multicolumn header on many lines; the second one with tabularx which equally distributes the spaces among the last 3 columns, leaving the header in one line.

documentclassreport
usepackage[T1]fontenc
usepackage[utf8]inputenc
usepackagebooktabs
usepackagecalc
usepackagearray
usepackagecolor
usepackagemakecell
usepackagetabularx
newcolumntypeC>centeringarraybackslashX
begindocument
%
% table 1 
% evenly alined
begintable[htbp]
centering
begintabularccccc
toprule
& & multicolumn3cReduced component sizes\
%cmidrule(r)3-5 
cmidrule3-5 
% multicolumn2cInternal mode count, $m$ &10&20&30&10&20&30\
%midrule
Component & Full size & $m=4$ & $m=8$ & $m=12$\
midrule
1 & 257 & 24 & 28 & 32 \
2 & 420 & 47 & 51 & 55 \
3 & 177 & 24 & 28 & 32 \
bottomrule
endtabular
captionInformation on component level degrees of freedom
labeltab:information-overview-academic-model
endtable
% 
begintable[htbp]
centering
begintabularccccc
toprule
& & multicolumn3cmakecellReduced component\ matrix sizes\ textcolorredtest text added\
%cmidrule(r)3-5 
cmidrule3-5 
% multicolumn2cInternal mode count, $m$ &10&20&30&10&20&30\
%midrule
Component & Full size & $m=4$ & $m=8$ & $m=12$\
midrule
1 & 257 & 24 & 28 & 32 \
2 & 420 & 47 & 51 & 55 \
3 & 177 & 24 & 28 & 32 \
bottomrule
endtabular
captionWith textbackslashtextttmakecell
labeltab:information-overview-academic-modelbis
endtable
begintable[htbp]
centering
begintabularxlinewidthccCCC
toprule
& & multicolumn3cReduced component matrix sizes textcolorredtest text added\
%cmidrule(r)3-5 
cmidrule3-5 
% multicolumn2cInternal mode count, $m$ &10&20&30&10&20&30\
%midrule
Component & Full size & $m=4$ & $m=8$ & $m=12$\
midrule
1 & 257 & 24 & 28 & 32 \
2 & 420 & 47 & 51 & 55 \
3 & 177 & 24 & 28 & 32 \
bottomrule
endtabularx
captionWith texttttabularx
labeltab:information-overview-academic-modelter
endtable
enddocument

Just for the sake of variety, here's a solution which (a) calculates the natural widths of columns 3, 4, and 5 and (b) uses the combined widths of the three columns (plus the intercolumn whitespace amount) to typeset the long header string in a way that allows for automatic line-breaking.

This approach keeps the tabular material nice and compact; this is generally considered to be a good thing.

Observe that I would place the headers "Component" and "Full size" at the top rather than at the bottom of the header material.

documentclassreport
usepackage[T1]fontenc
usepackage[utf8]inputenc
usepackagexcolor,booktabs,array,ragged2e
%% Create a new column type:
newcolumntypeC[1]>Centeringarraybackslashp#1

begindocument

begintable[htbp]
centering
begintabularccccc
toprule
& & multicolumn3cReduced component sizes\
cmidrule3-5 
Component & Full size & $m=4$ & $m=8$ & $m=12$\
midrule
1 & 257 & 24 & 28 & 32 \
2 & 420 & 47 & 51 & 55 \
3 & 177 & 24 & 28 & 32 \
bottomrule
endtabular
captionOP's original layout
labeltab:a
endtable


%% perform a few length calculations 
newlengthmylen
newlengthmylena
newlengthmylenb
settowidthmylena$m=4$
settowidthmylenb$m=12$
setlengthmylendimexpr2mylena+mylenb+4tabcolseprelax

begintable[htbp]
centering
begintabular@ccccc@
toprule
Component & Full size & 
multicolumn3Cmylen@Reduced component matrix sizes textcolorredtest text added\
cmidrule(l)3-5 
& & $m=4$ & $m=8$ & $m=12$\
midrule
1 & 257 & 24 & 28 & 32 \
2 & 420 & 47 & 51 & 55 \
3 & 177 & 24 & 28 & 32 \
bottomrule
endtabular
captionAutomatic line-breaking in cols 3 to 5
labeltab:b
endtable

enddocument